Question

the area of rectangular playground is 420msq. if it's length is increased by 7m and breadth is de 8 by 5 metre light area remains the same find the length and breadth of playground​

Answer 1

Sol. Let the length of a rectangular playground be ‘x’ m.

∵ The area of playground is 420 sq.m.

∴ length × breadth = 420

∴ x(breadth) = 420

∴ breadth = 420/x metre.

New length = (x + 7) m

New breadth = (420/x – 5) m

As per the given condition,

Area of new rectangle = Length × Breadth

420 = (x + 7) (420/x – 5)

∴ 420 = 420 – 5x + 2940/x – 35

∴ 420 – 420 = - 5x + 2940/x – 35

∴ 0 = - 5x + 2940/x – 35

Multiplying by x, we get

0 = - 5x2 + 2940 – 35x

∴ 5x2 + 35x – 2940 = 0

Dividing by 5, we get

x2 + 7x – 588 = 0

x2 – 21x + 28x – 588 = 0

∴ x (x – 21) + 28 (x – 21) = 0

∴ (x – 21) (x + 28) = 0

∴ x – 21 = 0 or x + 28 = 0

∴ x = 21 or x = -28

∴ The length of playground cannot be negative.

∴ x = 21

∴ 420/x = 420/21 = 20

∴ The length of a rectangular playground is 21 m and its breadth is 20 m.