Question

In the adjoining figure, ABCD is a square grassy lawn of area
729 m2. A path of uniform width runs all around it. If the area
of the path is 295 m2, find
(i) the length of the boundary of the square field enclosing
the lawn and the path.
(ii) the width of the path.​

Answer 1

Given,

Area of square ABCD = 729 m²

So, its side = √729 = 27 m

Let’s take the width of path = x m

Then,

Side of outer field = 27 + x + x = (27 + 2x) m

And, area of square PQRS = (27 + 2x)2 m²

Now,

Area of PQRS – Area of ABCD = Area of path

⇒ (27 + 2x)² m² – 729 m² = 295 m²

729 + 4x² + 108x – 729 = 295

4x2 + 108x – 295 = 0

By using the quadratic formula, we have

a = 4, b = 108 and c = -295

Hence,

Width of the path is 2.5 m

Now, side of square field PQRS = 27 + 2x

= (27 + 2 × 2.5) m

= 32 m

Therefore,

Length of boundary = 4 × side = 32 × 4 = 128 m

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