SOLUTION: the perimeter of a rectangle is 26 centimeters. the area of the rectangle remains the same if the length is decreased by 3 centimeters and the width is increased by 2 centimeters.

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Question 844240: the perimeter of a rectangle is 26 centimeters. the area of the rectangle remains the same if the length is decreased by 3 centimeters and the width is increased by 2 centimeters. what is the dimensions of the original rectangle?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
P = perimeter
L = length
W = width
formula for P is P = 2L + 2W
A = area
formula for A is A = LW

you are given that:
P = 26
This means that:
2L + 2W = 26

you know that LW = A, but you don't know what A is.
you are also given that (L-3)*(W+2) = A.
Since they are both equal to A, you can make LW equal to (L-3)*(W+2)
you get:
LW = (L-3) * (W+2)
simplify this equation to get:
LW = LW + 2L - 3W - 6
subtract LW from both sides of this equation to get:
0 = 2L - 3W - 6
Add 3W to both sides of this equation to get:
3W = 2L - 6
Divide both sides of this equation by 3 to get:
W = 2/3 * L - 2

you know that 2L + 2W = 26
replace W with 2/3 * L - 2 in that equation to get:
2L + 2 * (2/3 * L - 2) = 26
simplify to get:
2L + 4/3 * L - 4 = 26
add 4 to both sides of this equation to get:
2L + 4/3 * L = 30
Multiply both sides of this equation by 3 to get:
6L + 4L = 90
combine like terms to get:
10L = 90
divide both sides of this equation by 10 to get:
L = 9

go back to your original equation for P to get:
2L + 2W = 26
replace L with 9 to get:
18 + 2W = 26
subtract 18 from both sides of this equation to get:
2W = 8
divide both sides of this equation by 2 to get:
W = 4

your solution is:
L = 9
W = 4

Your perimeters becomes 2 * 9 + 2 * 4 = 18 + 8 = 26
The area is 9 * 4 = 36
subtract 3 from 9 and add 2 to 4 and you get:
The area is 6 * 6 = 36

The area remained the same when you subtracted 3 from the length and added 2 to the width.
The solution is good.
L = 9
W = 4