SOLUTION: I have a bunch of practice workbook questions that I'm struggling with. Here is another one. If somebody could please explain the answer and how you got to the answer. The area

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I have a bunch of practice workbook questions that I'm struggling with. Here is another one. If somebody could please explain the answer and how you got to the answer. The area      Log On


   

Question 806302: I have a bunch of practice workbook questions that I'm struggling with. Here is another one. If somebody could please explain the answer and how you got to the answer.
The area of a rectangle is 33m sq., and the length of the rectangle is 5m less than twice the width. Find the dimensions of the rectangle.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
+A+=+33+ m2
+L+=+2W+-5+ m
-----------------
The formula for area is
+A+=+L%2AW+
By substitution:
+A+=+%28+2W+-+5+%29%2AW+
+33+=+2W%5E2+-+5W+
+2W%5E2+-+5W+-+33+=+0+
Using the quadratic formula:
+W++=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+-5+
+c+=+-33+
+W++=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2+-+4%2A2%2A%28-33%29+%29%29+%2F+%282%2A2%29+
+W++=+%28+5+%2B-+sqrt%28+25+%2B+264+%29%29+%2F+4+
+W++=+%28+5+%2B-+sqrt%28+289+%29%29+%2F+4+ ( I can't use the negative square root )
+W+=+%28+5+%2B+17+%29+%2F+4+
+W+=+22%2F4+
+W+=+11%2F2+
and, since
+L+=+2W+-5+
+L+=+2%2A%2811%2F2%29+-5+
+L+=+11+-+5+
+L+=+6+
The rectangle is 6 m x 5.5 m
check:
+A+=+L%2AW+
+A+=+6%2A5.5+
+33+=+33+
OK