SOLUTION: The perimeter of a rectangle is 146 inches. The length is 7 inches shorter than three times the width. Find the length.

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Question 1063302: The perimeter of a rectangle is 146 inches. The length is 7 inches shorter than three
times the width. Find the length.
Found 3 solutions by addingup, josgarithmetic, MathTherapy:
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website!
perimeter = 2*width + 2*length, or the long way: width + width + length + length. In other words, all around the edge of the rectangle, what we call the perimeter.
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Length = 3W-7
So now we have:
2W+2(3W-7) = 146 distribute the 2 over the "stuff" in the parenthesis (Distributive Property of Multiplication):
2W+6W-14 = 146
8W = 160
W = 20
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Check:
2(20)+2(3*(20)-7)
40+106 = 146 Correct
:
John

Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website!
w Width
L length

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

The perimeter of a rectangle is 146 inches. The length is 7 inches shorter than three times the width. Find the length.

Let length be L and width, W
Then: 2(L + W) = 146______2(L + W) = 2(73)_____L + W = 73______W = 73 - L ------ eq (i)
Also, L = 3W - 7 ------- eq (ii)
L = 3(73 - L) - 7 ------ Substituting 73 - L for W in eq (ii)
L = 219 - 3L - 7
L + 3L = 219 - 7
4L = 212
L, or length =