A rectangular playground is 420 sq.m. If its length is increases by 7 m and breadth is decreased by 5 metres, the area remains the same. Find the length and breadth of the playground ?

12. A rectangular playground is 420 sq.m. If its length is increases by 7 m and breadth is decreased by 5 metres, the area remains the same. Find the length and breadth of the playground ?

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.