Question

I NEED HELP PLZ ASAP!!!!! In right triangle ABCD above, x = A. 6 B. 8 C. 6√2 D. 10 E. 13

Answer 1

Answer:

x=6

Step-by-step explanation:

Since this is a right triangle we can use  the Pythagorean theorem

a^2 + b^2 = c^2

where a and b are the legs and c is the hypotenuse

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

FOIL (x+2)^2 = x^2 +2x+2x+4 = x^2 +4x+4

FOIL (2x-2)^2 = 4x^2 -4x -4x+4 = 4x^2 -8x+4

Replacing these in to the equation

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

Combine like terms

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

Subtract 4 from each side

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

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

Subtract 2x^2 from each side

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

4x = 2x^2 -8x

Subtract 4x from each side

4x-4x = 2x^2 -8x-4x

0 = 2x^2 -12x

Factor out a 2x

0 = 2x(x-6)

Using the zero product property

2x =0  x-6 =0

x =0  x-6+6 = 0+6

x = 0  c=6