SOLUTION: Perimeter of a rectangle. The width of a rectangular playground is 2x-5 feet and the length is 3x+9 feet. Write a polynomial P(x) that represents the perimeter and then evaluate

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Question 124368: Perimeter of a rectangle. The width of a rectangular playground is 2x-5 feet and the length is 3x+9 feet. Write a polynomial P(x) that represents the perimeter and then evaluate this perimeter polynomial if x is 4 feet.
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Let W represent the width of the rectangle and L represent the length.
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The perimeter (P) is defined as the sum of the lengths of the sides of a polygon. In this case
the perimeter of this rectangle is found by adding the 4 sides. In equation form this is:
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P = W + L + W + L
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And by combining like terms on the right side this reduces to:
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P = 2W + 2L
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The problem tells you that the width W is equal to 2x - 5 feet. Substitute this for W in the
perimeter equation and it becomes:
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P = 2(2x - 5) + 2L
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The problem also tells you that the length L is equal to 3x + 9 feet. Substitute this for L in
the perimeter equation and it then becomes:
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P = 2(2x - 5) + 2(3x + 9)
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Do the two distributed multiplications on the right side to get:
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P = 4x - 10 + 6x + 18
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Combine the like terms on the right side ... the 4x and 6x combine to give 10x and the
-10 and the +18 combine to +8. Substitute these results and the perimeter equation
reduces to the polynomial form:
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P = 10x + 8 in units of feet
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That's the equation you needed to find. Then the problem asks if x is 4 feet, what is the
perimeter. Substitute 4 for x and you get:
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P = 10(4) + 8 = 40 + 8 = 48 feet
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check ... if x is 4 feet then the width (given by 2x - 5) is 3 feet and the length
(given by 3x + 9 is 21 feet. Therefore, the perimeter is 3 + 21 + 3 + 21 = 48 feet. That checks.
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Hope this helps you to understand the problem.
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