Question

A path of 5m wide runs around a square park of side 200m. Find the area
of the path. Also find the cost of cementing it at the rate of Rs. 300 per
10 square meters.

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Answer 1

$\underline\bold {\huge {ANSWER\::}}$

Area= 4100 sq. m

Cost = Rs. 1,23,000

Steps:-------

1. Find the area of the park.

As it is in the shape

of a square ,thus the area is equal to side X side .

2. After calculating the Area, find the outer length and the outer breadth .

Now , calculate the area of the outer rectangle .

Using the formula, length × breadth.

3. To find the area of the path , subtract the area of the Park from the area of the outer rectangle .

4. You have got the area of the path .

5. Multiply the cost of cementing by the area of the path.

6. This gives you the total cost of cementing the path.

7. Refer to the attachment for the full solution.

Answer 2

$\mathrm{\huge{\underline{\underline{Solution:}}}}$

$\textsf{Side of Square Field = 200 m } \\ \\ \sf{Area \: of \: Field = 200 × 200 \: m {}^{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = 40000 \: m {}^{2} \\ \\ \textsf{Outer Side = 200 + 5 + 5} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: = 210 \\ \\ \sf Area \: of \: Outer \: Square \\ \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf {Side}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf {210}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf 44100 \: m {}^{2} \\ \\ \therefore \sf Area \: of \: Path \\ \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf 44100 - 40000 \: m {}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf 4100 \: m {}^{2} \\ \\ \sf Cost \: of \: Cementing \: 10 \: m^2 = Rs. \: 300 \\ \sf Cost \: of \: Cementing \: 1 \: m^2 = Rs. \dfrac{30\cancel0}{1\cancel0} = Rs. \: 30 \\ \\ \sf \therefore Cost \: of \: Cementing \: the \: Path \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \implies 30 \times 4100 \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \implies Rs. \:123000$