original rectangle
Geometry
Level
pending
If the length of a rectangle is increased by 2 and its width is increased by 3, the area will increased by 58. If its length is decreased by 8 and its width is decreased by 6, the area will decreased by 88. Find the difference between the length and the width of the original rectangle.
The answer is 4.
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1 solution
If we call the length l and the width w , we see ( l +2)( w +3)= l w +58 l w + 2 w + 3 l +6= l w +58 2 w + 3 l =52.
We are also told ( l -8)( w -6)= l w -88 l w - 8 w - 6 l +48= l w -88 8 w + 6 l =136.
Solving these simultaneously we get l =12 and w =8. 12-8= 4