SOLUTION: A rectangle is half as wide as it is long. If both the length and width are decreased by 2 cm, the area decreases by 68 cm(squared) . Find the length of the original rectangle.
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Question 202617: A rectangle is half as wide as it is long. If both the length and width are decreased by 2 cm, the area decreases by 68 cm(squared) . Find the length of the original rectangle.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let the original length = L and the original width = W, so that the original area:
but the problem says that the "...rectangle is half as wide as it is long.", so this can be expressed as:
Substitute this into the first equation and you get:
Now, if we subtract 2 cm from the length (L-2) and 2 cm from the width (W-2) the area is decreased by 68 sq.cm. (A-68). Lets find the new area:
but substitute and
Simplifying:
Subtract from both sides.
Subtract 4 from both sides.
Divide both sides by -3.
and
The original length of the rectangle is 24 cm.
Check:
Original area:
Substitute L=24 and W=12
sq.cm.
Now the new area is:
Substitute L=24 and W=12
sq.cm.
The difference is:
=sq.cm.
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