What is the area of a rectangle with length (2x+2), width (x) and a diagonal of 13?

1 Answer
Jan 1, 2016

The area of such rectangle is 60.

Explanation:

Using the Pythagorean Theorem a^2+b^2=c^2, we substitute the expressions into the equation:

x^2+(2x+2)^2=13^2
x^2+4x^2+8x+4=169
5x^2+8x-165=0

Factor the equation:

(5x^2-25x)+(33x-165)=0
5x(x-5)+33(x-5)=0
(5x+33)(x-5)=0

The two solutions we find are -33/5 and 5. Since we cannot have a negative width, we immediately discard the negative solution, leaving us with x=5.

Now we simply solve for the area by substituting x with 5, and we get our answer:

2(5)+2=10+2=12
5*12=60