SOLUTION: The area of a rectangular blanket is 33 square feet. The blanket's length is (3x+8) feet and the blanket's width is 3x feet. Find the dimensions of the blanket. Thanks for your

Question 495798: The area of a rectangular blanket is 33 square feet. The blanket's length is (3x+8) feet and the blanket's width is 3x feet. Find the dimensions of the blanket.
Thanks for your help.

Answer by kingme18(98) (Show Source): You can put this solution on YOUR website!
The area of a rectangle is length times width. Therefore, if you multiply your length times width, you'll get 33.

Multiplication is commutative, so I'm going to rewrite the left hand side:
Distribute the 3x:
When we're dealing with quadratics, we like to have them equal 0, so subtract 33 on both sides:
We're going to want to factor or use the quadratic formula, but first, we can divide through by 3 to make the numbers a little smaller. I'm dividing EVERYTHING by 3:

If you factor, you get , and you solve:
and get
and get .
If you use the quadratic formula, you'll end up with the same answers.

Your blanket's width is 3x. It would make no sense for x to equal , because the width would be , and your blanket can't have a negative dimension. Therefore, x=1. Then the width is and the widtch is , which makes sense, because the area is , which is what you knew at the beginning. Thus, the width is 3 and the length is 11.
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