Question

In a rectangular Park of dimensions 50m×40m rectangular Pond is constructed so that the area of grass strip of uniform breadth surrounding the pond would be 1184 m square. find the length and breadth of the pond

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the width of the grass strip be x m.

Length of pond = (50 - 2x) m.

Breadth of pond = (40 - 2x) m.

According to the Question,

Area of park - Area of pond = Area of grass strip.

⇒ (50 × 40) - (50 - 2x)(40 - 2x) = 1184

⇒ 2000 - 2000 + 184x - 4x² = 1184

⇒ x² - 45x + 296 = 0

⇒ x² - 37x - 8x + 296 = 0

⇒ x(x - 37) - 8(x - 37) = 0

⇒ (x - 37) (x - 8) = 0

⇒ x = 8, 37 (37 is rejected)

⇒ x = 8

Length of pond = 50 - 2 × 8 = 34 m

Breadth of pond = 40 - 2 × 8 = 24 m.