27.) Because the area is 60, we know that the two side lengths, x and x + 4 will multiply to equal that.
In other words,
x(x+4) = 60
Distribute the x
x^2 + 4x = 60
Complete the square:
1.) Take the middle term, 4, divide it by 2, then square it. You get 4 again.
2.) Add 4 on both sides of the equation:
x^2 + 4x + 4 = 64
3.) Factor the left side, you'll find that it is a perfect trinomial.
(x + 2)(x + 2)= 64
4.) Simplify (x + 2)^2 = 64
5.) Square root both sides:
(x + 2) = +/- 8
Because side lengths cannot be negative, it must be positive 8.
6.) x + 2 = 8
7.) Subtract 2 on both sides, you'll see that x = 6 :)
