What is the perimeter of a rectangle whose length is 2.5 greater than its width with an area of 37.5 square inches show work?

Answer 1

Suppose width = W inches.

Then length, L = W + 2.5 inches.

Area = L*W = (W + 2.5)*W which is 37.5 sq inches.

Therefore W2 + 2.5W - 37.5 = 0

Multiplying by 2, to get rid of the fraction,

2W2 + 5W - 75 = 0

(2W +15)(W - 5) = 0

So W = -73.5 or W = 5

Since W is a length, it cannot be negative, so W = 5 inches

Then L = W + 2.5 = 7.5 inches

Therefore, the perimeter is 2*(L+W) = 2*(7.5 + 5) = 2*12.5 = 25 inches.