Question

The longer leg of a righttriangle is 3 ft longer than the shorter leg. The hypotenuse is 6 ft longer than the shorter leg. Find the side lengths of the triangle.Length of the shorter leg: Length of the longer leg:Length of the hypotenuse:

Answer 1

First, let's set up the legs:

Let L be the longer leg, S the shorter and H the hypothenuse:

S = S

L = S + 3

H = S + 6

The triangle is a right triangle, so, using Pythagorean Theorem:

`H^=√(L^2+S^2)`

Replacing H, L and S values on the formula:

`\lparen S+6)^2=S^2+\left(S+3\right)^2`

Solving the expression:

S² + 12S + 36 = S² + S² + 6S + 9

S² - 6S - 27 = 0

(S - 9)(S + 3)

S = -3 or S = 9

Measures can't be negative so we will use 9. Plug it back into the original 3 equations:

S = S

S = 9 (length of the shorter leg)

L = S + 3

L = 9 + 3

L = 12 (length of the longer leg)

H = S + 6

H = 9 + 6

H = 15 (length of the hypotenuse)