SOLUTION: the legnth of a rectangle is 4 cm less than twice its width. its perimeter is 40 cm. find the length and width of the rectangle.

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Question 162024: the legnth of a rectangle is 4 cm less than twice its width. its perimeter is 40 cm. find the length and width of the rectangle.
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
This is a problem of having 2 equations with 2 unknowns. Anytime you have at least as many equations as you have unknowns, you can solve the problem!
Equation #1 is derived from the first statement: "The length of a rectangle is 4 cm less than twice its width." Let L be the length and W be the width. Then you can write the following equation:
Equation #1: L=2W-4
Equation #2 is derived from the second statement: "Its perimeter is 40 cm." Let P be the Perimeter. The Perimeter of any rectangle is given by:
P=2L%2B2W
You are given P, so you can re-write this as:
Equation #2: 40=2L%2B2W
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Now you have developed 2 equations and have 2 unknowns. You are in fat city. Substitute The expression for L from Equation #1 into Equation #2:
40=2%282W-4%29%2B2W
Solve for W:
40=4W-8%2B2W
6W=48
highlight%28W=8+cm%29
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Now that you have W, plug that into Equation #1 to find L:
40=2L%2B2%288%29
Solve for L:
40=2L%2B16
2L=24
highlight%28L=12cm%29
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Good Luck,
tutor_paul@yahoo.com