# 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*).

## Practice Questions

- 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

*a*^{2}+*b*^{2}=*c*^{2}, 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:**a*^{2}+ 8^{2}= 17^{2}*a*^{2}+ 64 = 289*a*^{2}= 225*a*= 15Hence, 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,

*a*^{2}+*b*^{2}=*c*^{2}(where*a*and*b*are the legs of the triangle and*c*is the hypotenuse). Substituting the given sides into the equation gives you12

^{2}+ 16^{2}=*c*^{2}144 + 256 =

*c*^{2}400 =

*c*^{2}20 =

*c*Therefore,

*c*= 20 miles.