Question

The floor of a rectangular hall has a perimeter
250 m. If the cost of painting the four walls at
the rate of 10 per m' is 15000, then find the
height of the hall
Hint Area of the four walls = Lateral surface area ​

Answer 1

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$\color{red}\huge{\underline{\underline{\mathfrak{Question:-}}}}$

The floor of a rectangular hall has a perimeter

250 m. If the cost of painting the four walls at

the rate of 10 per m' is 15000, then find the

height of the hall?

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$\color{blue}\huge{\underline{\underline{\mathfrak{Answer}}}}$

${\blue{\bold{ Height \:is\:6\:metres}}}$

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Given:-

• Perimeter=250 m
• Cost of painting four walls:- 15000 rs
• Rate of painting per metre square is 10 rs

${\blue{\bold{ Now }}}$

Lateral surface area = $\frac{Total\:cost}{Cost\:per\: meter\:square}$

$\implies$ $\frac{15000}{10}$

$\implies$1500 m²

Perimeter of floor=250 m

$\implies$2(l+b)=250

$\implies$(l+b)=$\frac{250}{2}$

$\implies$(l+b)=125........(1)

${\blue{\bold{ We\:know\:that }}}$

${\blue{\bold{ Lateral\:surface\:area\:of\:cuboid=2h(l+b) }}}$

$\implies$1500=2h(l+b)

$\implies$1500=2h(125)

[FROM EQUATION 1]

$\implies$$\frac{1500}{125}=2h$

$\implies$12=2h

$\implies$$\frac{12}{2}$=h

$\implies$6 m=h

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Hope it helps

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

Let length, breadth, and height of the rectangular hall be l, b, and h respectively.

Area of four walls = 2lh + 2 bh

= 2 (l + b) h

Perimeter of the floor of hall = 2(l + b)

= 250 m

Area of four walls = 2(l + b) h = 250h m²

Cost of painting per square meter area = Rs.10

Cost of painting 250h square meter area = Rs (250 h x 10) = Rs.2500h

However, it is given that the cost of paining the walls is Rs. 15000.

15000 = 2500h

Or h = 6

• Therefore, the height of the hall is 6 m.