Question 108418: A rectangle is twice as long as it is wide. If its length and width are both decreased by 4 cm, its area is decreased by 164 cm2. Find its original dimensions.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Let x = the original width
:
"A rectangle is twice as long as it is wide."
2x = original length
Then
2x^2 = original area
:
If its length and width are both decreased by 4 cm, its area is decreased by 164 cm2.
(2x - 4) by (x - 4) = new dimensions
(2x^2 - 12x + 16)= new area
:
Original area - New area = 164 sq/cm
2x^2 - (2x^2 - 12x + 16) = 164
:
2x^2 - 2x^2 + 12x - 16 = 164 removing brackets, changes the signs
:
12x = 164 + 16; conveniently, the 2x^2 are eliminated, add 16 to both sides
12x = 180
12x = 180/12
x = 15 cm is the original width
Then
2(15) = 30 cm is the original length
:
Check by subtracting the new area from the original area
(30*15) - (26*11) =
450 - 286 = 164; confirms our solution
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