SOLUTION: The length of a rectangular piece of carpet is 5 meters less than twice its width. Find dimensions of the carpet if its area is 33 square meters.

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Question 531717: The length of a rectangular piece of carpet is 5 meters less than twice its width.
Find dimensions of the carpet if its area is 33 square meters.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +L+=+2W+-+5+
+A+=+33+
+L%2AW+=+33+
(2) +W+=+33%2FL+
Substitute (2) into (1)
(1) +L+=+2%2A%2833%2FL%29+-+5+
(1) +L%5E2+=+66+-+5L+
(1) +L%5E2+%2B+5L+-+66+=+0+
Use quadratic formula
L+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+5+
+c+=+-66+
L+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A%28-66%29+%29%29%2F%282%2A1%29+
L+=+%28-5+%2B-+sqrt%28+25+%2B+264+%29%29%2F2+
L+=+%28-5+%2B-+sqrt%28+289+%29%29%2F2+
L+=+%28-5+%2B+17%29%2F2+
+L+=+12%2F2+
+L+=+6+ ( ignore the negative root )
(2) +W+=+33%2FL+
(2) +W+=+33%2F6+
(2) +W+=+5.5+
The dimensions are 5.5 m x 6 m
check:
(1) +L+=+2%2A%2833%2FL%29+-+5+
(1) +6+=+2W+-+5+
(1) +6+=+2%2A5.5+-+5+
(1) +6+=+11+-+5+
(1) +6+=+6+
OK