SOLUTION: please help me answer the following problem: the length of a rectangle is 5cm greater than 3 times its width. the area of the rectangle is 22cm^2. find the length and the width

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Question 611354: please help me answer the following problem:
the length of a rectangle is 5cm greater than 3 times its width. the area of the rectangle is 22cm^2. find the length and the width of the rectangle.
thanks so much i don't know how o set it up and the steps for doing it!!!! thanks!!!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let L = the length in cm
Let W = the width in cm
Let A = the area of the rectangle in cm2
-----------
given:
+L+=+3W+%2B+5+
+A+=+22+ cm2
+A+=+L%2AW+
+A+=+%28+3W+%2B+5+%29%2AW+
+22+=+3W%5E2+%2B+5W+
+3W%5E2+%2B+5W+-+22+=+0+
--------------------
Use the quadratic formula
+W+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+3+
+b+=+5+
+c+=+-22+
+W+=+%28-5+%2B-+sqrt%28+5%5E2+-+4%2A3%2A%28-22%29+%29%29+%2F+%282%2A3%29+
+W+=+%28-5+%2B-+sqrt%28+25+%2B+264+%29%29+%2F+%282%2A3%29+
+W+=+%28-5+%2B-+sqrt%28+289+%29%29+%2F+6+
+W+=+%28-5+%2B+17+%29+%2F+6+
+W+=+12%2F6+
+W+=+2+
( ignore the negative root- can't have negative length )
and, since
+L+=+3W+%2B+5+
+L+=+3%2A2+%2B+5+
+L+=+6+%2B+5+
+L+=+11+
The length is 11 cm and the width is 2 cm