Measurements of a right triangle

Question

One leg of a right triangle is four inches longer than the other. The hypotenuse is 20 inches. Whatever are the measurements of the triangle?

Answer 1

x = one leg

x + 4 = other leg

(x + 4)² + x² = 20² Pythagorean's theorem a² + b² = c²

x² + 8x + 16 + x² = 400

2x² + 8x - 384 = 0 Subtract 400 from both sides of the equation

2(x² + 4x - 192) = 0 Factor two from everything

Using the quadratic equation you get the results x =−16 and x = 12.

Since the legs of the right triangle cannot be negative x = 12 is the answer we use along with 12 + 4 = 16.

The legs of the right triangle are 12 and 16 with a hypotenuse of 20.