SOLUTION: The perimeter of a rectangle is 36m. If its length is increased by 1m and the width is increased by 2m, its area will increase by 30m2. Find the area of the original rectangle.

Algebra ->  Finance -> SOLUTION: The perimeter of a rectangle is 36m. If its length is increased by 1m and the width is increased by 2m, its area will increase by 30m2. Find the area of the original rectangle.      Log On


   



Question 1006038: The perimeter of a rectangle is 36m. If its length is increased by 1m and the width is increased by 2m, its area will increase by 30m2. Find the area of the original rectangle.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +A+ = area of original rectangle
The formula for perimeter is:
+P+=+2L+%2B+2W+
+36+=+2L+%2B+2W+
+L+%2B+W+=+18+
+L+=+18+-+W+
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Let +A+ = area
+A+=+L%2AW+
+A+=+%28+18+-+W+%29%2AW+
+A+=+18W+-+W%5E2+
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You are given that:
+A+%2B+30+=+%28+L+%2B+1+%29%2A%28+W+%2B+2+%29+
+A+%2B+30+=+%28+18+-+W+%2B+1+%29%2A%28+W+%2B+2+%29+
+A+%2B+30+=+%28+-W+%2B+19+%29%2A%28+W+%2B+2+%29+
+A+=+-W%5E2+%2B+19W+-+2W+%2B+38+-+30+
+A+=+-W%5E2+%2B+17W+%2B+8+
------------------------
By substitution:
+18W+-+W%5E2+=+-W%5E2+%2B+17W+%2B+8+
+18W+=+17W+%2B+8+
+W+=+8+
and
+L+=+18+-+W+
+L+=+18+-+8+
+L+=+10+
and
+A+=+L%2AW+
+A+=+10%2A8+
+A+=+80+
The original area was 80 m2
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check:
+A+%2B+30+=+%28+L+%2B+1+%29%2A%28+W+%2B+2+%29+
+A+%2B+30+=+%2810+%2B+1+%29%2A%28+8+%2B+2+%29+
+A+=+11%2A10+-+30+
+A+=+110+-+30+
+A+=+80+
OK