SOLUTION: the length of a rectangle is three times its width. if the width is diminished by 1 inch and the length is increased by 3 inches, the area of the new rectangle is 72 square inches.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: the length of a rectangle is three times its width. if the width is diminished by 1 inch and the length is increased by 3 inches, the area of the new rectangle is 72 square inches.      Log On


   

Question 249348: the length of a rectangle is three times its width. if the width is diminished by 1 inch and the length is increased by 3 inches, the area of the new rectangle is 72 square inches. find the dimensions of the original rectangle.
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
L=3W
AREA=LW
FOR THE NEW RECTANGLE:
L=L+3
W=W-1
(L+3)=3(W-1)
L+3=3W-3
L=3W-3-3
L=3W-6
LW=72
(3W+6)W=72
3W^2+6W-72=0
3(W^2+2W-24)=0
3(W+6)(W-4)=0
W-4=0
W=4 ANS. FOR THE NEW WIDTH.
4-1=3 FOR THE ORIGINAL WIDTH.
L*4=72
L=72/4
L=18 ANS. FOR THE NEW LENGTH.
18+3=21 ANS. FOR THE ORIGINAL LENGTH.
PROOF:
4*18=72
72=72