The length of a rectangle is 10 inches greater than the width. The area of the rectangle is 75 square inches. Find the dimensions.

Question

The length of a rectangle is 10 inches greater than the width. The area of the rectangle is 75 square inches. Find the dimensions.

Answer 1

w: x

L: x+10

(x)(x+10)=75

x²+10x=75

x²+10x-75=0

(x+15)(x-5)=0

for the width, it cannot be -15, so it has to be the other factor, 5.

So the width is 5 and the length is 15.

Answer 2

Let l = w+ 10 then the area is w(w+10)=75 w² _{+ 10 w = 75 w}² _{+10 w - 75 = 0 This factors into (w+10)(w-5) = 0 hence the only factor that is good is w = 5 and this means l = 15. So those are the dimensions.}