Question 638398: the perimeter of a tablecloth is 360 inches. the length is 36 inches greater than the width. find the width.
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! The perimeter of a rectangle is length+length+width+width, or 2L+2W. The length is 36 inches greater than the width, so L=W+36. In our first equation (2L+2W), replace the L with W+36. So, 2(W+36)+2W=360. Using the distributive property, multiply 2 by what's in the parenthesis: 2W+2*36 = 2W+72. So, our equation looks like this:
2W+72+2W=360
Add 2W and 2W together
4W+72=360
We want to get W by itself on the left side of the equal sign, so to do that, first subtract both sides of the equal sign by 72:
4W+72-72=360-72
This gives us
4W=288
Now, divide both sides by 4, which will get rid of the 4 on the left side and leave us with W:
W=288/4
Divide 288 by 4:
W=72
So, our width is 72 inches
To determine our length, substitute 72 for W in the equation L=W+36:
L=72+36
Therefore, L = 108, which is our length.
To verify, replace the L and W in the formula for the perimeter of a rectangle, with 108 and 72. If that answer = 360, then the length and width are correct:
2(108)+2(72) =
216+144 =
360
So, our length and width are correct
Final Answer: Length - 108 inches
Width - 72 inches
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