SOLUTION: The perimeter of a rectangle is 148 feet. The length if 14ft. greater than one and a half times the width. What is the length of the rectangle?

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Question 573811: The perimeter of a rectangle is 148 feet. The length if 14ft. greater than one and a half times the width. What is the length of the rectangle?
Answer by mathsmiles(68) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 148 ft. The formula for perimeter of a rectangle is L + L + W + W = 2L + 2W = P

So we have our first equation:
2L + 2W = 148

L is 14ft more than W x 1.5 OR
L = 14 + 1.5W

What is L?

Let's use substitution from the second equation for L and use that in the first equation.
2L + 2W = 148
2(14 + 1.5W) + 2W = 148
Multiply out the parens
28 + 3W + 2W = 148
Combine terms:
28 + 5W = 148
Subtract 28 from each side:
5W = 120
Divide both sides by 5:
W = 24

Now we need to find the length L
L = 14 + 1.5 (W)
L = 14 + 1.5 (24)
L = 14 + 36
L = 50

Checking:
2(50) + 2(24) = 148?
100 + 48 = 148?
148 = 148 Correct!

Re-read the question so you give the answer in the form it's asked including the correct unit of measure. :-) Good luck!!