a rectangle is 4 centimeters longer than it is wide.

Question

a rectangle is 4 centimeters longer than it is wide. If the length and width are both decreased by 2 centimeters, the area is decreased by 24 square centimeters. Find the dimensions of the original rectangle.

Answer 1

L=4+W

(L-2)(W-2)=A-24= (4+W-2)(W-2)=(W+2)(W-2)=W^2-4

A=W^2-4+24=W^2+20

LW=A=(4+W)W=4W+W^2 = W^2+20

4W=20

W=20/4=5 cm =Width

L=9 cm = Length

A=9x5 = 45

A= 3x7=21 =45-24 after W&L decreased by 2