the length of the longer leg of a right triangle is 2 ft longer than the length of the shorter leg x. The hypotenuse is 2 ft shorter than twice the length of the shorter leg

Question

a. write an equation in terms of x that represents the given relationship

b. solve the equation to find the dimensions of the given shape

Answer 1

You are working with a right triangle. Use

a^2 + b^2 = c^2. The sides are x, (x+2) and the hypotenuse is (2x - 2)

(X+2)^2 + (x)^2 = (2x-2)^2

(x+2)(x+2) +x^2 = (2x-2)(2x-2)

x^2+2x+2x+4+x^2 =. 4x^2 - 4x -4x + 4

2x^2 +4x + 4. =. 4x^2. - 8x + 4

2x^2. + 4x. =. 4x^2. -8x

0. = 2x^2 - 12x. 0 = 2x(x - 6)

x = 0 or x = 6. Sides will be 6, 8 and 10