SOLUTION: The perimeter of a rectangle is 30 cm. If its length is decreased by 3 cm and its width is increased by 5 cm, the area of the rectangle will decrease by 8 cm^2. Find the area of th

Question 1067623: The perimeter of a rectangle is 30 cm. If its length is decreased by 3 cm and its width is increased by 5 cm, the area of the rectangle will decrease by 8 cm^2. Find the area of the original rectangle.
thx
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
let a = area
let l = length
let w = width
Since the perimeter is 30,
2w + 2l = 30
divide each side by 2
w + l = 15
add - l to each side
w = 15 - l
Below we see ( length - 3 )(width + 5) = original area - 8
(l-3)(w+5)=a-8
Since lw = a ,
(l-3)(w+5)=lw-8
lw + 5*l -3*w -15 = lw -8
add -lw to each side
5*l -3*w -15 = -8
add 15 to each side
5*l -3*w = 7
since w = 15 - l, substitute 15 - l for w in 5*l -3*w = 7
5*l -3*(15 - l) = 7
5*l -45 + 3*l = 7
8*l -45 = 7
add 45 to each side
8*l = 52
divide each side by 8
l = 52/8 = 6.5
since w = 15 - l, w = 15 - 6.5 = 8.5
The area of the original rectangle = 6.5 * 8.5 = 55.25
Notice that area of the alternate rectangle is
(length -3)(width + 5) = 3.5 * 13.5 = 47.25
The difference in the area of the rectangles is 55.25-47.25 = 8

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