Question 162429This question is from textbook
: if the length of a certain rectangle were increased by 2ft and the widh decreased by 1ft,the area would be decreased by 2sq ft. if the length were decreased by 2ft and the width increased by 2ft,the area would be increased by 16sq.ft. find the dimensions of the rectangle.....
This question is from textbook
Answer by Anthea Lawn(22)   (Show Source):
You can put this solution on YOUR website! Let the length of the rectangle be x and the width = y
The area of the rectange, A, is xy. ie the width times the length.
Now : (x + 2)(y - 1) = xy - 2 (from the first bit of information)
and : (x - 2)(y + 2) = xy + 16 (from the second bit of information)
From the first equation
xy + 2y - x - 2 = xy - 2
rearranging :
2y = x ----------(1)
From the second equation :
xy - 2y + 2x - 4 = xy + 16
2x - 2y = 20
x - y = 10 ------------(2)
Combining that with (1) gives 2y - y = 10 therefore y = 10
and from either (1) or (2) that means x = 20
In summary the rectangle is 20 X 10 = 200 square feet
Increase the length by 2 and decrease the width by 1 and the area is 22 X 9 = 198 sq feet.
Decrease the length by 2 and increase the width by 2 and the area is 18 X 12 = 216 sq feet.
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