Two cross roads, each of width $5 m$ , run at the 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 $R s .105 p e r m^{2}$ .

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Solution

width $= 5 m$

length of first parallel road $70 m$

area of first road $70 \times 5 = 350 s q . m$

length of second road $45 m$

area of second road $= 45 \times 5 = 225 s q . m$

area of the common part of cross road with $5 m$ width that lies at the

center of the park $5 \times 5$ = $225 s q . m$

area of roads $=$ area of first road $+$ area of second cross road $-$ common area

$\begin{matrix} = (350 + 225) - 25 = 575 - 25 = 550 s q m \end{matrix}$

cost of the construction per $s q . m$ $= R s . 105$

total cost $= 550 \times 105 = R s 57750$

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