Question

the length of a rectangle is 3 feet longer than its width. if its width is decreased by 3 feet and its width is increased by 4 feet, its area would be increased by 8 square feet. what is the length of the rrctanglr?

Answer 1

Let l,w be the length and width of rectangle

Given l = w+3.

Let the area be A= l*w = (w+3)*w

Also given that (l-3)*(w+4) = A+8

(w+3-3)*(w+4) = (w+3)*w + 8

`w*(w+4) = w^(2) +3w+8`

`w^(2) +4w = w^(2)+3w+8`

Subtracting
`w^(2)` and 3w on both sides

`w^(2)+4w-w^(2)-3w = 8`

w=8 feet

l= w+3 = 8+3 = 11 feet

Hence length of rectangle = 11 feet.