SOLUTION: The perimeter of a rectangle is 72 m. If the width were doubled and the length were increased by 9 m, then the perimeter would be 114 m. What are the dimensions?

Algebra ->  Linear-equations -> SOLUTION: The perimeter of a rectangle is 72 m. If the width were doubled and the length were increased by 9 m, then the perimeter would be 114 m. What are the dimensions?      Log On


   

Question 263075: The perimeter of a rectangle is 72 m. If the width were doubled and the length were increased by 9 m, then the perimeter would be 114 m. What are the dimensions?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 72 m.
If the width were doubled and the length were increased by 9 m, then the perimeter would be 114 m.
What are the dimensions?
:
Original perimeter equation:
2L + 2W = 72
:
meters added equation
2(L+9) + 2(2W) = 114
2L + 18 + 4W = 114
2L + 4W = 114 - 18
2L + 4W = 96
:
Subtract the original equation from the above equation
2L + 4W = 96
2L + 2W = 72
--------------Subtraction eliminates L, find W
2W = 24
W = 24%2F2
W = 12 m is the original width
:
Find the original length
2L + 2(12) = 72
2L + 24 = 72
2L = 72 - 24
2L = 48
L = 48%2F2
L = 24 m is the original length
;
:
Check in the added meter equation
2(24+9)) + 2(24) =
66 + 48 = 114