SOLUTION: Helping my child do her math and could use some help. The length of a rectangle is 9 cm less than twice its width. If the area of the rectangle is 11cm squared, find the dimens

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Question 863010: Helping my child do her math and could use some help.
The length of a rectangle is 9 cm less than twice its width. If the area of the rectangle is 11cm squared, find the dimensions of the rectangle.
Many thanks in advance,

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = the width
+2w+-+9+ = the length
------------------------
The area = ( length ) x ( width )
+A+=+%28+2w+-+9+%29%2Aw+
+11+=+%28+2w+-+9+%29%2Aw+
+2w%5E2+-+9w+=+11+
+2w%5E2+-+9w+-+11+=+0+
Use the quadratic formula
+w+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+-9+
+c+=+-11+
+w+=+%28+-%28-9%29+%2B-+sqrt%28+%28-9%29%5E2+-+4%2A2%2A%28-11%29+%29%29+%2F+%282%2A2%29+
+w+=+%28+9+%2B-+sqrt%28+81+%2B+88+%29%29+%2F+4+
+w+=+%28+9+%2B-+sqrt%28+169+%29%29+%2F+4+
+w+=+%28+9+%2B+13+%29+%2F+4+
+w+=+11%2F2+
and
+2w+-+9+=+2%2A%2811%2F2%29+-+9+
+2w+-+9+=+11+-+9+
+2w+-+9+=+2+
------------------
The dimensions are:
5.5 cm x 2 cm
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check:
+A+=+%28+2w+-+9+%29%2Aw+
+A+=+2%2A5.5+
+A+=+11+ cm2
OK