2 Marks Questions

Question

Two cross roads, each of width 5 m, run at right angles through the centre of a rectangular park of length 70 m and breadth 45 m and parallel to its sides. Find the area of the roads. Also find the cost of constructing the roads at the rate of ₹ 105 per m^2.

Accepted Answer

Clearly, area of the cross roads is the area of shaded portion, i.e., the area of the rectangle $PQRS$ and the area of the rectangle $EFGH.$ But while doing this, the area of the square $KLMN$ is taken twice, which is to be subtracted once to get the required area.
Now, $P Q=5 \mathrm{~m}$ and $P S=45 \mathrm{~m}$
$\mathrm{EH}=5 \mathrm{~m} \text { and } \mathrm{EF}=70 \mathrm{~m}$
$\mathrm{KL}=5 \mathrm{~m} \text { and } \mathrm{KN}=5 \mathrm{~m}$
Therefore, area of the path $=$ Area of the rectangle $PQRS\ + $ area of the rectangle $EFGH\ -$ Area of the square $KLMN$
$=\mathrm{PS} \times \mathrm{PQ}+\mathrm{EF} \times \mathrm{EH}-\mathrm{KL} \times \mathrm{KN}$
$=(45 \times 5+70 \times 5-5 \times 5) \mathrm{m}^2$
$=(225+350-25) \mathrm{m}^2=550 \mathrm{~m}^2$
Hence, cost of constructing the path $=₹ 105 \times 550=₹ 57,750$

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