SOLUTION: the perimeter of a rectangle with length, l and width, w is given by P = 2w +21 if the perimeter of the rectangle is 105 feet and the length is 35 feet, what is the width? show all

Question 471395: the perimeter of a rectangle with length, l and width, w is given by P = 2w +21 if the perimeter of the rectangle is 105 feet and the length is 35 feet, what is the width? show all work
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The equation for the perimeter P of a rectangle is:
.
P = 2*L + 2*W
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in which L = Length and W = Width. You are told that for a given rectangle P = 105 ft and L = 35 ft and are asked to find W.
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First, substitute 105 for P and the equation becomes:
.
105 = 2*L + 2*W
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Then substitute 35 for L, and then the equation becomes:
.
105 = 2*35 + 2*W
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Do the multiplication in the first term of the right side of this equation. 2 times 35 equals 70 and the equation then is:
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105 = 70 + 2*W
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Get rid of the 70 on the right side by subtracting 70 from both sides:
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105 - 70 = 70 - 70 + 2*W
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Do the two subtractions. On the left side 105 minus 70 is 35 and on the right side 70 minus 70 is zero. Therefore, the equation is reduced to:
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35 = 0 + 2*W
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or just:
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35 = 2*W
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Finally, solve for W by dividing both sides of the equation by 2:
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35/2 = 2*W/2
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35 divided by 2 is 17 1/2 or 17.5 and 2*W/2 becomes just W. Therefore, the solution for W is just:
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17.5 = W
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Transpose (reverse sides) to get the equation in standard form with the unknown on the left and you have:
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W = 17.5
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and don't forget to add the units of "feet".
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W = 17.5 feet
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Hope this helps you to see and understand some of the processes used to solve equations.

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