SOLUTION: Originally the dimensions of a rectangle were 20 cm by 23 cm. When both dimensions were decreased by the same amount, the area of the rectangle decreased by 120 cm (squared). Fin

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Question 250461: Originally the dimensions of a rectangle were 20 cm by 23 cm. When both dimensions were decreased by the same amount, the area of the rectangle decreased by 120 cm (squared). Find the dimensions of the new rectangle.
Found 2 solutions by drk, checkley77:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We reduce length and width by the same amount to get
(20-X) and (23-x). Now the area is reduced by 120, so,
460+-+%2820-X%29%2823-X%29+=+120
foiling the left gives us
460+-+%28x%5E2+-+43X+%2B+460%29+=+120
-x%5E2+%2B+43X+-+120+=+0+
or
x%5E2+-+43X+%2B+120+=+0+
by factoring, we get
%28x-3%29%28x-40%29+=+0
X = 3 or X = 40.
Since 40 is too big,
we are left with X = 3.
The new rectangle dimensions are:
17 x 20

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(20-x)(23-x)=20*23-120
460-43x+x^2=460-120
x^2-43x+460-460+120=0
x^2-43x+120=0
(x-40)(x-3)=0
x-3=0
x=3 cm. is the decrease in size of both sides.
Proof:
(20-3)(23-3)=20*23-120
17*20=460-120
340=340