The perimeter of rectangle is 80m. If the breadth increased by 2m and

1.	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.
Answer» Answer: 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

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.

Answer»

Answer:

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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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.​

breadth = 10m

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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.