The area of the school is
165(300) = 49500 square feet.
The area of the parking lot with the school is
(165+75)(300+75) = 240(375) = 90000 square feet. This means the area of just the parking lot is
90000-49500 = 40500 square feet.
The area of the new expanded lot will be doubled; this means it will be
2(40500) = 81000 square feet. Adding back the area of the school, this means the total lot will be
81000+49500 = 130500 square feet.
The width will be 375+x and the length will be 240+x; this gives us
130500 = (375+x)(240+x)
Multiplying the binomials gives us
130500 = 90000+375x+240x+x²
130500 = 90000+615x+x²
To solve this, we first set it equal to 0. We do this by subtracting 130500 from each side:
130500-130500 = 90000+615x+x²-130500
0 = x²+615x-40500
We will use the quadratic formula:
Substituting our values for a, b and c,
We do not use negative numbers for measurement, so x = 60.