**Question:**

In a rectangular park of dimensions 50 m × 40 m, a rectangular pond is constructed so that the area of grass strip of uniform width surrounding the pond would be 1184 m2. Find the length and breadth of the pond.

**Solution:**

It is given that the dimensions of rectangular park is 50 m × 40 m.

∴ Area of the rectangular park = 50 × 40 = 2000 m2

Area of the grass surrounding the pond = 1184 m2

Now,

Area of the rectangular pond

= Area of the rectangular park − Area of the grass surrounding the rectangular pond

= 2000 − 1184

= 816 m2

Let the uniform width of the surrounding grass be *x*.

∴ Length of the rectangular pond = (50 − 2*x*) m

Breadth of the rectangular pond = (40 − 2*x*) m

Now,

Area of rectangular pond = 816 m2

∴ (50 − 2*x*) × (40 − 2*x*) = 816

⇒ 2000 − 80*x *− 100*x* + 4*x*2 = 816

⇒ 4*x*2 − 180*x* + 2000 − 816 = 0

⇒ 4*x*2 − 180*x *+ 1184 = 0

⇒ *x*2 − 45*x *+ 296 = 0

⇒* x*2 − 37*x* − 8*x* + 296 = 0

⇒ *x*(*x *− 37) − 8(*x *− 37) = 0

⇒ (*x* − 8)(*x* − 37) = 0

⇒ *x* − 8 = 0 or *x* − 37 = 0

⇒* x *= 8 or *x* = 37

For *x* = 37,

Length of rectangular pond = 50 − 2 × 37 = −24 m, which is not possible

So, *x* ≠ 37

Therefore, *x* = 8.

When *x* = 8,

Length of the rectangular pond = 50 − 2 × 8 = 50 − 16 = 34 m

Breadth of the rectangular pond = 40 − 2 × 8 = 40 − 16 = 24 m.

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