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# The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs 10 per m^2 is Rs 15000, find the height of the hall.

Q : 3        The floor of a rectangular hall has a perimeter $\small 250\hspace {1mm} m$. If the cost of painting the four walls at the rate of Rs 10 per $\small m^2$ is Rs 15000, find the height of the hall.

[Hint : Area of the four walls $\small =$ Lateral surface area.]

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Given,

Perimeter of rectangular hall = $\small 250\hspace {1mm} m$

Cost of painting the four walls at the rate of Rs 10 per $\small m^2$ = Rs 15000

Let the height of the wall be $h\ m$

$\therefore$ Area to be painted = $Perimeter\times height$

$= 250h\ m^2$

$\therefore$ Required cost = $250h\times10\ m^2 = 15000\ m^2$

$\\ \implies 2500h = 15000 \\ \implies h = \frac{150}{25} = 6\ m$

Therefore, the height of the hall is $6\ m$

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