Justin 2 Algebra

Question

The hypotenuse of a right triangle measures 20 yards. If one leg of the triangle is four yards longer than the other leg, find the measures of the legs.

Answer 1

Hi Justin,

You can solve this problem in more than one way. You could use the Pythagorean theorem with the sides of x and (x + 4) : x² + (x+ 4)² = 20²

However, an easier way may be based on similar triangles. The hypotenuse of 20 is divisible by 5, so this is a scaled triangle of a 3 -4 -5 triangle.

Since the hypotenuse is multiplied by 4, the other sides will be as well:

3 • 4 = 12

4 • 4 = 16

5 • 4 = 20

The leg measurements will be 12 yards and 16 yards (and 16 is 4 more than 12).

Also: 12² + 16² = 20²

144 + 256 = 400