GED Math Extra Prep: Right Triangles
If you understand the Pythagorean theorem, then you should have no trouble answering questions on the GED Math test that deal with right-triangle problems.
If you can’t recognize a right-triangle problem, look for the word hypotenuse (that’s a dead giveaway), or word problems that contain directions that are at a 90-degree angle from each other (like due north and due west).
- The hypotenuse of a right triangle is 17 inches. If one of the legs of the triangle is 8 inches long, what is the length of the other leg?
A. 8 inches
B. 12 inches
C. 15 inches
D. 19 inches
- A hiker walks 16 miles due north and then turns and walks 12 miles due west. How many miles is the hiker from his starting point?
Answers and Explanations
- The correct answer is Choice C.
Because the triangle is a right triangle, you can use the Pythagorean theorem, which states that a2 + b2 = c2, where side c equals the length of the hypotenuse and a and b are the legs. Let the missing side equal a. Substitute the given values into the equation and solve for a:
a2 + 82 = 172
a2 + 64 = 289
a2 = 225
a = 15
Hence, Choice (C) is the correct answer.
- The correct answer is 20 miles.
Because the hiker’s path has formed two sides of a right triangle, the distance from home is the length of the hypotenuse, so use the Pythagorean theorem, a2 + b2 = c2 (where a and b are the legs of the triangle and c is the hypotenuse). Substituting the given sides into the equation gives you
122 + 162 = c2
144 + 256 = c2
400 = c2
20 = c
Therefore, c = 20 miles.