The perimeter of rectangle is 80m. If the breadth increased by 2m and the length decreased by 2m, the area of the rectangle increases by 36m². Assuming the length to be x, obtain an equation. Also, find the length and breadth of the rectangle.
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Let the length of the field = x
breadth = y
perimeter = 2(x+y) =80
⇒ x+y = 80/2
⇒ x+y = 40
Area = xy
If the length is decreased by 2m and breadth is increased by 2m,
new length = (x-2)
new breadth = (y+2)
area = (x-2)(y+2) = xy + 2x -2y - 4
this area is 36 m² more than earlier area. So
(xy + 2x -2y - 4) - (xy) = 36
⇒2x -2y - 4 =36
⇒2x - 2y = 36+4 = 40
⇒ x-y = 20
Add the 2 equations, we get
2x = 60
⇒ x = 30m
y = 10m
Hence length = 30m
breadth = 10m
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