Question

The perimeter of a rectangular field is 84. If the length of the field is increased by 2 metres and breadth is decreased by 4 metres, the area is decreased by 32 sq m. Find the length and breadth of the rectangular field.

Answer 1

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Answer 2

Answer:

The length and breadth of the rectangular field is 18 m and 24 m respectively.

Step-by-step explanation:

Let the length of rectangle be x

Let the breadth of rectangle be y

Area of rectangle = $Length \times Breadth$

                             = $xy$

Perimeter of rectangle = $2(l+b)$

                                      = $2(x+y)$

The perimeter of a rectangular field is 84.

So,  $2(x+y)=84$

$2x+2y=84$  ----A

The length of the field is increased by 2 meters

So, New Length = x+2

The  breadth is decreased by 4 meters.

So, New Breadth = y-4

New Area = $(x+2)(y-4)$

Since we are given that the area is decreased by 32 sq.m.

So,  $xy-(x+2)(y-4)=32$

$xy-(xy-4x+2y-8)=32$

$4x-2y+8=32$

$4x-2y=32-8$

$4x-2y=24$ ---B

Substitute the value of 2y from A in B

$4x-(84-2x)=24$

$4x-84+2x=24$

$6x-84=24$

$6x=24+84$

$6x=108$

$x=\frac{108}{6}$

$x=18$

So, Length = 18 m

Substitute the value of x in B

$4(18)-2y=24$

$72-2y=24$

$72-24=2y$

$48=2y$

$24=y$

Breadth = 24 m

Hence The length and breadth of the rectangular field is 18 m and 24 m respectively.