The first option because you would need to get rid of 2/3 by dividing it on both sides, then you would subtract 57 to get x
Longer leg = x + 4
Shorter leg = x
Hypotenuse = x + 8
Using Pythagorean Theorem:
a^2 + b^2 = c^2
(x + 4)^2 + x^2 = (x + 8)^2
x^2 + 8x + 16 + x^2 = x^2 + 16x + 64
2x^2 + 8x + 16 = x^2 + 16x + 64
2x^2 +8x = x^2 + 16x + 48
2x^2 - 8x = x^2 + 48
x^2 - 8x = 48
x^2 - 8x - 48 = 0
You can complete the square from here or use the quadratic formula.
Completing the square:
x^2 - 8x = 48
x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2
x^2 - 8x + 16 = 48 + 16
(x - 4)(x - 4) = 64 or (x - 4)^2 = 64
x - 4 = +√64 OR x - 4 = -√64
x - 4 = +8 OR x - 4 = -8
x = 12 OR x = -4
However, you can't use negative 4 as a length because your length needs to be a positive.
So x will be 12.
Shorter leg: 12
Longer leg: 12 + 4
Hypotenuse: 12 + 8
You get imaginary roots for this equation.
x=4-5i
x=4+5i
Answer:
-5.2
Step-by-step explanation:
