SOLUTION: The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. What
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Question 245167: The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. What are the length and the width? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The perimeter of a rectangle is six times the width.
:
perimeter:
2L + 2W = 6W
2L = 6W - 2W
2L = 4W
Simplify, divide both sides by 2
L = 2W
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If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches.
2(L+4) + 2(W+7) = 160
2L + 8 + 2W + 14 = 160
2L + 2W + 22 = 160
2L + 2W = 160 - 22
2L + 2W = 138
Simplify, divide by 2
L + W = 69
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What are the length and the width?
From the 1st statement we know L=2W; replace L with 2W
2W + W = 69
3W = 69
W =
W = 23 is the width
then
L = 2(23)
L = 46 is the width
:
:
Check solution in the 1st statement:
"The perimeter of a rectangle is six times the width."
2(46) + 2(23) = 6(23)
92 + 46 = 138;
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YOu can check the solution using the 2nd statement
"If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. "
