Question

The length of a rectangle is 10 feet longer than it is wide. if each side is increased 10 feet, then the area is multiplied by 4. what was the size of the original rectangle?

Answer 1

Suppose:
width=x ft
length=(x+10) ft
Area:
x(x+10) ft²

Given that the sides are increased by 10, then the new dimensions will be:
width=(x+10) ft
length=(x+20) ft
thus the area will be:
(x+10)(x+20)=4×(x^2+10x)
solving for x we get:
x=-10 or x=20/3
thus the original width=20/3 and length=(10+20/3)=50/3 ft