The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. The length of the hypotenuse is 6ft more than twice the length of the shorter leg. Find the side lengths of the triangle. a. Find the length of the shorter side
b. Find the length of the longer side
c. Find the length of the hypotenuse
d. Find the side lengths of the triangle.

Shorter side = 10 feet

Longer side = 24 feet

Hypotenuse = 26 feet

The side lengths of the triangle are 10ft, 24ft and 26ft.

Step-by-step explanation:

Let the length of the shorter leg be x.

The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. This will be: = 2x + 4

The length of the hypotenuse is 6ft more than twice the length of the shorter leg. This will be: = 2x + 6

Note that the square of the hypothenuse will be equal to the square of the other two sides. This will be:

x² + (2x + 4)² = (2x + 6)²

x² + (2x + 4)(2x + 4) = (2x + 6)(2x + 6)

x² + 4x² + 8x + 8x + 16 = 4x² + 12x + 12x + 36

x² + 4x² + 16x + 16 = 4x² + 24x + 36

5x² + 16x + 16 = 4x² + 24x + 36

Collect like terms

5x² - 4x² + 16x - 24x + 16 - 36 = 0

x² - 8x - 20 = 0

x² - 10x + 2x - 20 = 0

x(x - 10) + 2(x - 10) = 0

Therefore, x - 10 = 0

x = 10

a. length of the shorter side = 10ft

b. Length of the longer side = 2x + 4 = 2(10) + 4 = 20 + 4 = 24ft

c. length of the hypotenuse = 2x + 6 = 2(10) + 6 = 20 + 6 = 26ft

d. The side lengths of the triangle are 10ft, 24ft and 26ft.