Question

In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed, so that the area of the grass surrounding the pond would be 1184 m2 . (4) (i) If the distance between pond and lawn is x m. Find the length and breadth of rectangular pond​

Answer 1

Answer:

Let x = Distance between the boundaries of the lawn and the pond.

Length of pond =(50−2x) m and breadth of pond =(40−2x)m

Area of pond = Area of lawn − Area of grass around pond.

∴(40−2x)(50−2x)=(50)(40)−1184

2000−1184=2000−180x+4x

2

⇒x

2

−45x+296=0

⇒x

2

−8x−37x+296=0

⇒x(x−8)−37(x−8)=0

⇒(x−8)(x−37)=0

x=37,x=8