Answer
8 in.
Work Step by Step
The area of $\triangle$ ABC is 40$in^{2}$
$\angle$C = 90$^{\circ}$, AC= x, BC = x+2
We need to find out the value of x
The area of right angle triangle with legs of length a and b is given by A = $\frac{1}{2}$ab
From given right triangle ABC
Lengths of legs a= x+2
b=x
Area of $\triangle$ ABC = $\frac{1}{2}$ab
40 $in^{2}$ = $\frac{1}{2}$x*(x+2)
80 = $x^{2}$ + 2x
$x^{2}$ + 2x - 80 = 0
$x^{2}$ + 10x - 8x - 80 = 0
x(x+10) - 8(x+10) = 0
(x-8)(x+10) = 0
x =8,-10
Therefore the value of x is 8in. because it cant be negative.
