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Sum

A path 5 m wide runs along inside a square park of side 100 m. Find the area of the path. Also, find the cost of cementing it at the rate of Rs. 250 per 10 m^{2}.

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#### Solution

Let ABCD be the square park of side 100 m. The shaded region represents the path 5 m wide.

PQ = 100 – (5 + 5) = 90 m

Area of square ABCD = (side)^{2} = (100)^{2} m^{2} = 10000 m^{2}

Area of square PQRS = (side)^{2} = (90)^{2} m^{2} = 8100 m^{2}.

Therefore, area of the path = (10000 − 8100) m^{2} = 1900 m^{2}

Cost of cementing 10 m^{2} =Rs. 250

Therefore, cost of cementing 1 m^{2 }= Rs. `250/10`

So, cost of cementing 1900 m^{2 }= Rs. `250/10 xx 1900` = Rs. 47,500.

Concept: Problems based on Perimeter and Area

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