SOLUTION: the perimeter of a rectangle is 26cm.The area of the rectangle remains unaltered if the lenght is decreased by 3cm and width is increased by 2cm.Find the dimension of the original

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Question 850106: the perimeter of a rectangle is 26cm.The area of the rectangle remains unaltered if the lenght is decreased by 3cm and width is increased by 2cm.Find the dimension of the original rectangle
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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the perimeter of a rectangle is 26cm. The area of the rectangle remains unaltered if the lenght is decreased by 3cm and width is increased by 2cm.
Find the dimension of the original rectangle
:
2L + 2W = 26
simplify, divide by 2
L + W = 13
L = (13-W); use this form for substitution
Area = LW
and
New area = old area
(L-3)*(W+2) = LW
Foil
LW + 2L - 3W - 6 = LW
Subtract LW from both sides
2L - 3W + 6 = 0
Replace L with (13-W)
2(13-W) - 3w - 6 = 0
26 - 2W - 3W - 6 = 0
-5W + 20 = 0
-5W = -20
W = -20/-5
W = 4 cm is the original Width
then
13 - 4 = 9 cm is the length
:
You can check the area of each, ensure they are equal