Question 157074: Solve the problem. The perimeter of a rectangle is 62 m. If the width were doubled and the length were increased by 21 m, the perimeter would be 120 m. What are the length and width of the rectangle?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The perimeter of a rectangle is 62 m. If the width were doubled and the length
were increased by 21 m, the perimeter would be 120 m. What are the length and
width of the rectangle?
;
Write an equation for each statement, simplify as much as you can:
:
"The perimeter of a rectangle is 62 m."
2L + 2W = 62
Simplify, divide equation by 2:
L + W = 31
L = (31-W); use for substitution
:
"If the width were doubled and the length were increased by 21 m, the perimeter would be 120 m."
2(2W) + 2(L+21) = 120
4W + 2L + 42 = 120
4W + 2L = 120 - 42
4W + 2L = 78
Simplify divide by 2
2W + L = 39
:
Using the 1st equation, substitute (31-W) for L
2W + (31-W) = 39
2W - W = 39 - 31
W = 8 m is the original width
then
L = 31 - 8
L = 23 is the original length
;
:
Check solution in the statement:
"If the width were doubled and the length were increased by 21 m, the perimeter would be 120 m."
New rectangle dimensions: 44 by 16
2(16) + 2(44) = 120; confirms our solutions
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