{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T07:10:05+00:00","modifiedTime":"2016-03-26T07:10:05+00:00","timestamp":"2022-09-14T17:46:02+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"},"slug":"geometry","categoryId":33725}],"title":"Similar-Triangle Word Problems — Practice Geometry Questions","strippedTitle":"similar-triangle word problems — practice geometry questions","slug":"similar-triangle-word-problems-practice-geometry-questions","canonicalUrl":"","seo":{"metaDescription":"When two triangles are similar, this means that their sides are in proportion. The following word problems ask you to use the properties of similar triangles—an","noIndex":0,"noFollow":0},"content":"<p>When two triangles are <i>similar,</i> this means that their sides are in proportion. The following word problems ask you to use the properties of similar triangles—and a little bit of algebra—to find the solutions.</p>\n<p class=\"Remember\">Similar triangles are different only in size. The corresponding angles still have the same measure.</p>\n<h2 id=\"tab1\" >Practice questions</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">The lengths of the sides of a triangle are 16, 23, and 31. If the perimeter of a similar triangle is 280, find the length of that triangle's longest side.</p>\n </li>\n <li><p class=\"first-para\">In triangle <i>RST</i>, <i>W</i> is a point on </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501379.image0.png\" height=\"23\" alt=\"image0.png\" width=\"25\"/>\n<p class=\"child-para\">and <i>Y</i> is a point on </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501380.image1.png\" height=\"23\" alt=\"image1.png\" width=\"25\"/>\n<p class=\"child-para\">such that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501381.image2.png\" height=\"25\" alt=\"image2.png\" width=\"63\"/>\n<p class=\"child-para\">If <i>WS</i> = 5, <i>RW</i> = <i>x</i> + 7, <i>YS</i> = <i>x</i>, and <i>TY</i> = <i>x</i> + 3, solve for <i>x.</i></p>\n </li>\n</ol>\n<h2 id=\"tab2\" >Answers and explanations</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">124</p>\n<p class=\"child-para\">If two triangles are similar, their sides are in proportion. Suppose you call the original triangle <i>A</i> and the new triangle <i>B.</i> The proportion would be as follows:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501382.image3.png\" height=\"177\" alt=\"image3.png\" width=\"131\"/>\n </li>\n <li><p class=\"first-para\">3</p>\n<p class=\"child-para\">A line that intersects two sides of a triangle and is parallel to the third side of the triangle creates two similar triangles. If two triangles are similar, their sides are in proportion, and the parts of their sides are also in proportion:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501383.image4.png\" height=\"237\" alt=\"image4.png\" width=\"151\"/>\n </li>\n</ol>","description":"<p>When two triangles are <i>similar,</i> this means that their sides are in proportion. The following word problems ask you to use the properties of similar triangles—and a little bit of algebra—to find the solutions.</p>\n<p class=\"Remember\">Similar triangles are different only in size. The corresponding angles still have the same measure.</p>\n<h2 id=\"tab1\" >Practice questions</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">The lengths of the sides of a triangle are 16, 23, and 31. If the perimeter of a similar triangle is 280, find the length of that triangle's longest side.</p>\n </li>\n <li><p class=\"first-para\">In triangle <i>RST</i>, <i>W</i> is a point on </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501379.image0.png\" height=\"23\" alt=\"image0.png\" width=\"25\"/>\n<p class=\"child-para\">and <i>Y</i> is a point on </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501380.image1.png\" height=\"23\" alt=\"image1.png\" width=\"25\"/>\n<p class=\"child-para\">such that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501381.image2.png\" height=\"25\" alt=\"image2.png\" width=\"63\"/>\n<p class=\"child-para\">If <i>WS</i> = 5, <i>RW</i> = <i>x</i> + 7, <i>YS</i> = <i>x</i>, and <i>TY</i> = <i>x</i> + 3, solve for <i>x.</i></p>\n </li>\n</ol>\n<h2 id=\"tab2\" >Answers and explanations</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">124</p>\n<p class=\"child-para\">If two triangles are similar, their sides are in proportion. Suppose you call the original triangle <i>A</i> and the new triangle <i>B.</i> The proportion would be as follows:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501382.image3.png\" height=\"177\" alt=\"image3.png\" width=\"131\"/>\n </li>\n <li><p class=\"first-para\">3</p>\n<p class=\"child-para\">A line that intersects two sides of a triangle and is parallel to the third side of the triangle creates two similar triangles. If two triangles are similar, their sides are in proportion, and the parts of their sides are also in proportion:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501383.image4.png\" height=\"237\" alt=\"image4.png\" width=\"151\"/>\n </li>\n</ol>","blurb":"","authors":[{"authorId":8986,"name":"Allen Ma","slug":"allen-ma","description":" <p><b>Allen Ma </b>and<b> Amber Kuang </b>are math teachers at John F. Kennedy High School in Bellmore, NY. Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8986"}},{"authorId":8987,"name":"Amber Kuang","slug":"amber-kuang","description":" <p><b>Allen Ma </b>and<b> Amber Kuang </b>are math teachers at John F. Kennedy High School in Bellmore, NY. Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8987"}}],"primaryCategoryTaxonomy":{"categoryId":33725,"title":"Geometry","slug":"geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Practice questions","target":"#tab1"},{"label":"Answers and explanations","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":207513,"title":"Geometry: 1001 Practice Problems For Dummies Cheat Sheet","slug":"1001-geometry-practice-problems-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/207513"}},{"articleId":144555,"title":"Circle Basics for Geometry Problems","slug":"circle-basics-for-geometry-problems","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/144555"}},{"articleId":144556,"title":"Coordinate Geometry Formulas","slug":"coordinate-geometry-formulas","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/144556"}},{"articleId":144557,"title":"Geometry Practice Problems with Triangles and Polygons","slug":"geometry-practice-problems-with-triangles-and-polygons","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/144557"}},{"articleId":143448,"title":"Formulas for Geometric Solids Problems","slug":"formulas-for-geometric-solids-problems","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/143448"}}],"fromCategory":[{"articleId":230077,"title":"How to Copy an Angle Using a Compass","slug":"copy-angle-using-compass","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230077"}},{"articleId":230072,"title":"How to Copy a Line Segment Using a Compass","slug":"copy-line-segment-using-compass","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230072"}},{"articleId":230069,"title":"How to Find the Right Angle to Two Points","slug":"find-right-angle-two-points","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230069"}},{"articleId":230066,"title":"Find the Locus of Points Equidistant from Two Points","slug":"find-locus-points-equidistant-two-points","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230066"}},{"articleId":230063,"title":"How to Solve a Two-Dimensional Locus Problem","slug":"solve-two-dimensional-locus-problem","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230063"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281917,"slug":"geometry-1001-practice-problems-for-dummies-free-online-practice","isbn":"9781118853269","categoryList":["academics-the-arts","math","geometry"],"amazon":{"default":"https://www.amazon.com/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1118853261-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/geometry-1001-practice-problems-for-dummies-cover-9781118853269-193x255.jpg","width":193,"height":255},"title":"Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"8986\">Allen Ma</b> and <b data-author-id=\"8987\">Amber Kuang</b> are math teachers at John F. 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Similar-Triangle Word Problems — Practice Geometry Questions

By: Allen Ma and Amber Kuang and

Updated: 03-26-2016

From The Book: Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)

Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)

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When two triangles are similar, this means that their sides are in proportion. The following word problems ask you to use the properties of similar triangles—and a little bit of algebra—to find the solutions.

Similar triangles are different only in size. The corresponding angles still have the same measure.

Practice questions

The lengths of the sides of a triangle are 16, 23, and 31. If the perimeter of a similar triangle is 280, find the length of that triangle's longest side.
In triangle RST, W is a point on

and Y is a point on

such that

If WS = 5, RW = x + 7, YS = x, and TY = x + 3, solve for x.

Answers and explanations

124

If two triangles are similar, their sides are in proportion. Suppose you call the original triangle A and the new triangle B. The proportion would be as follows:
3

A line that intersects two sides of a triangle and is parallel to the third side of the triangle creates two similar triangles. If two triangles are similar, their sides are in proportion, and the parts of their sides are also in proportion:

About This Article

This article is from the book:

Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice) ,

About the book authors:

Allen Ma and Amber Kuang are math teachers at John F. Kennedy High School in Bellmore, New York. Allen, who has taught geometry for 20 years, is the math team coach and a former honors math research coordinator. Amber has taught all levels of mathematics, from algebra to calculus, for the past 14 years.

This article can be found in the category:

Geometry ,