a rectangular playground is 420sq.m.if jts length is increases by 7 meters and breadth is decreases by 5 meters then the area remains the same.find the length and breadth of the playground.
Answers
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.