A rectangle is three times as long as it is wide. If its length and width are both decreased by 2cm, its area is decreased by 36cm^2. Make a sketch and find its original dimensions.

Question

A rectangle is three times as long as it is wide. If it’s length and width are both decreased by 2 cm, it’s area is decreased by 36 cm². Make a sketch and find its original dimensions.

Answer 1

let L = the length and W = the width of the rectangle. According the problem we have L = 3W

so the area of the rectangle is A = 3W*W = 3W^2 cm^2

if we decrease the two dimentions of the rectangle by 2, we will have (L-2)(W-2) = 3W^2 -36

substituting on the first side where L = 3W the first side becomes;  (3W-2)(W-2) = 3W^2 - 6W - 2W + 4 -->>

3w^2 - 8W + 4 = 3W^2 - 36  --->>>  -8W = -40  --->>>  W = 5 cm and L = 15 cm ( because L=3W)

So the area is 3*5^2  = 3*25 = 75 cm^2  or 5*15 = 75 cm^2

check  (5-2)(15-2) = 3*13 = 39 and this is 36 less than 75