Question

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

Answer 1

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`