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

1. 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
2. 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

1. 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.

2. 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.