SOLUTION: The length of a rectangle is 4 cm less than 3 times its width. If the lenght is increased by 8 cm and the width is decreased by 2 cm, the perimeter will be 100 cm. Find the dimensi

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Question 62096: The length of a rectangle is 4 cm less than 3 times its width. If the lenght is increased by 8 cm and the width is decreased by 2 cm, the perimeter will be 100 cm. Find the dimensions of the original rectangle.
Answer by joyofmath(189) About Me  (Show Source):
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The length of a rectangle is 4 cm less than 3 times its width. If the lenght is increased by 8 cm and the width is decreased by 2 cm, the perimeter will be 100 cm. Find the dimensions of the original rectangle.
Let W be the width of the original rectangle.
Let L be the length of the original rectangle. Then, L=3W-4.
If the perimeter becomes 100 when L is increased by 8 and when W is decreased by 2 then:
Old perimeter = 2%28W%2BL%29.
New perimeter = 2%28W-2%2BL%2B8%29+=+100.
We use the fact that L=3W-4 to replace L in the new perimeter equation with W-2.
So, 2%28W-2%2B%283W-4%29%2B8%29+=+100.
Or, 2%28W-2%2B3W-4%2B8%29+=+100.
Or, 2W-4%2B6W-8%2B16+=+100.
Or, 8W%2B4+=+100.
Or, 8W+=+96.
So, W=12.
L=3W-4+=+3%2812%29-4+=+32.
So, L=32.
Verify:
If L is increased by 8 and W is decreased by 2 then L=40 and W=10. So, the perimeter is 2%2AL%2AW+=+100.