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

Algebra ->  Geometry-proofs -> 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       Log On


   

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) About Me  (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.

%283x%2B8%29%2A3x=33
Multiplication is commutative, so I'm going to rewrite the left hand side: 3x%2A%283x%2B8%29=33
Distribute the 3x: 9x%5E2%2B24x=33
When we're dealing with quadratics, we like to have them equal 0, so subtract 33 on both sides: 9x%5E2%2B24x-33=0
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: 3x%5E2%2B8x-11=0

If you factor, you get %283x%2B11%29%28x-1%29=0, and you solve:
3x%2B11=0 and get x=-11%2F3
x-1=0 and get x=1.
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 -11%2F3, because the width would be 3%2Aexpr%28-11%2F3%29=-11, and your blanket can't have a negative dimension. Therefore, x=1. Then the width is 3%2A1=3 and the widtch is 3%2A1%2B8=3%2B8=11, which makes sense, because the area is 3%2A11=33, which is what you knew at the beginning. Thus, the width is 3 and the length is 11.