Question

The hypotenuse of a right triangle is 10 inches long. The longer leg is 2 inches longer than the shorter leg. Find the side lengths of the triangle.

Answer 1

Answer: Shorter leg = 6 inches

Longer leg = 6+2 = 8 inches

Step-by-step explanation:

Let the shorter leg bw represented by x.

Therefore, the longer leg will be x+2.

The hypothenuse is 10inches

We should note that in Pythagoras theorem, the square of the longer and shorter side equals the square of the hypothenuse. This will be:

x² + (x+2)² = 10²

x² + x² + 4x + 4 = 100

2x² + 4x = 100 - 4

2x² + 4x = 96

2x² + 4x - 96 = 0

x² + 2x - 48 = 0

x² + 8x - 6x - 48 = 0

x(x + 8) -6(x + 8) = 0

x - 6 = 0

x = 0+6.

x = 6

Shorter leg = 6 inches

Longer leg = 6+2 = 8 inches