SOLUTION: The lenght of a rectangle is 4 yards less than 5 times the width. If the perimeter is 184 yards find the lenght and the width of the reftangle

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Question 887329: The lenght of a rectangle is 4 yards less than 5 times the width. If the perimeter is 184 yards find the lenght and the width of the reftangle
Answer by algebrapro18(249) (Show Source):
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Let the length of the rectangle be L and let the width be W. Now we know that the length of the rectangle is 4 yards less than 5 times the width. An equation to express this would be:

L=5W-4

We also know that the perimeter is 184 yards and that to find the perimeter of a rectangle is 2l + 2w. We know that:

2L+2W = 184

Since we know an equation for the length we can plug that into the second equation and solve for Width.

2L+2W = 184 Plug in L=5W-4
2(5W-4)+2W = 184 Distribute
10W-8+2W = 184 Combine like terms
12W-8 = 184 Add 8 to both sides
12W = 192 Divide both sides by 12
W = 16

So we know that the width of the rectangle is 16 yards. We can now plug back into our equation for length to find the length.

L=5W-4
L=5(16)-4
L=76
So we found that the width is 16 yards and the length is 76 yards.