Question

The area of a rectangular playground is 420sq.m. If its length is increased by 7m and breadth is decreased by 5m,the area remains the same. Find the length and breadth of the playground

Answer 1

Let x and y be the length and breadth of the given rectangle

$Area = xy = 420$

We now increase its length by 7m and decrease its breadth by 5m

$Area = (x+7)(y-5)$

Since the area is equal in both cases, we can equate them

$xy = (x+7)(y-5)$

$xy=xy+7y-5x-35$

$7y-5x=35$

$\frac{7*420}{x} -5x=35$

$2940-5x^2=35x$

$x^2+7x-588=0$

$x^2+28x-21x-588 = 0$

$x(x+28)-21(x+28)=0$

$(x+28)(x-21)=0$

x = -28   or    x = 21

Since length cant be negative, we can say that

x = 21 m

y = 20 m

Hence length of the play ground is 21m and breadth is 20m

HOPE IT HELPS!!

Answer 2

Answer:

The length is 21.

The breadth is 20.