SOLUTION: The dimensions of a garden are in whole numbers. If the length is reduced by 3 and the width reduced by 1 then the area is reduced by half. What were the dimensions and area of t
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Question 206365: The dimensions of a garden are in whole numbers. If the length is reduced by 3 and the width reduced by 1 then the area is reduced by half. What were the dimensions and area of the original rectangle.
I know the answer but cannot find the math to get to it! Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The dimensions of a garden are in whole numbers.
If the length is reduced by 3 and the width reduced by 1 then the area is reduced by half.
What were the dimensions and area of the original rectangle.
:
Let L = original length
Let W = original width
LW = original area
:
(L-3) = new length
(W-1) = new width
New area = (L-3)*(W-1) = (LW - L - 3W + 3)
:
Original area = twice new area
LW = 2(LW - L - 3W + 3)
:
LW = 2LW - 2L - 6W + 6
:
2LW - LW - 2L - 6W + 6 = 0
:
LW - 2L = 6W - 6
:
L(W - 2) = 6W - 6
L =
Find a value for W that produces an integer value for L
W = 3
L =
L = 12
:
original: 12 by 3
original area = 36
:
Check solution
New area: 9 * 2 = 18, half the original
