Question

The floor of a rectangular hall has a perimeter 250 m. If the cost of panting the four walls at the rate of Rs.10 per m^2 is Rs.15000, find the height of the hall. [Hint: Area of the four walls = Lateral surface area.]

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Answer 1

$\huge\star{\underline{\mathtt{\red{A}\pink{n}\green{s}\blue{w}\purple{e}\orange{r}}}}$

$\longrightarrow$$\sf\pink{Lateral\:surface\:area\:=\:(Perimeter\:of\:floor)\:×\:height\:=\:250hm2}$

$\longrightarrow$$\sf\red{and}$

$\longrightarrow$$\sf\orange{cost\:=\:Rate\:×\:area}$

$\longrightarrow$$\sf\blue{15000\:=\:10\:×\:250h}$

$\longrightarrow$$\sf\frac\purple{2500}{15000} = h$

$\longrightarrow$$\sf\green{h\:=\:6m}$

Answer 2

Given:

Perimeter=250m

⇒Area of 4 walls =2lh+2bh

=2(b+l)h

⇒Perimeter of floor of wall =2l+2b

⇒2(l+b)=250 m

∴ Area of 4 walls =2(l+b)h

=250h m

2

⇒Cost of painting per m

2

area = Rs. 10

⇒Cost of painting 250h m

2

area = Rs(250h×10)

= Rs.2500h

⇒Painting cost of walls = Rs. 15000

⇒2500h=15000

⇒h=

2500

15000

⇒h=6m