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 m2 is ` 15000, find the height of the hall.​

Answer 1

Given -

• Perimeter of hall is 250 m

• Rate per m² is ₹10

• Total cost is ₹15000

To Find -

• Height of hall

Formulae used -

• LSA of rectangle

Solution -

In the question, we are given with the perimeter of a rectangular hall & also the rate per m² and total cost and we need to find the height of the hall. For that, we will apply the formula of lateral surface area of rectangle. First we will divide the total cost by the rate per m² after that, we will apply the formula then will take height to another side then we will solve the further question.

Let -

The height of hall be h m

So -

Perimeter = 250 m

Total cost = ₹15000

Rate per m² = ₹10

Now -

$\sf \longrightarrow \frac{total \: cost}{rate}$

$\sf \longrightarrow \dfrac{1500 \cancel{0}}{1 \cancel{0}}$

$\sf \longrightarrow \: 1500 \: { \: m}^{2}$

At the end -

$\sf \longrightarrow \: 2(l \: + \: b)h \: = 1500 \\ \\ \sf \longrightarrow \: 2(l \: + \: b) \: = 1500 \: \times \: h \\ \\ \sf \longrightarrow \: 250 \: m \: = 1500 \: \times \: h \\ \\ \sf \longrightarrow \: h \: = \dfrac{150 \cancel{0}}{25 \cancel{0}} \\ \\ \sf \longrightarrow \: h \: = \cancel \dfrac{150}{250} \\ \\ \sf \longrightarrow \: h \: = 6 \: m$

$\therefore$ The height of the hall is 6 m

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Answer 2

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 m2 is ` 15000, find the height of the hall.

To Find:-

• Find the height.

Solution:-

• Let the height be x

Given ,

• Perimeter = 250 m

• Area of 4 walls = 2( l + b )h

• Cost of painting is 2500

Now ,

We have to find the height:-

$\sf\longrightarrow \: Painting \: cost \: of \: walls = 1500$

$\sf\longrightarrow \: 2500h = 15000$

$\sf\longrightarrow \: h = \cancel\dfrac { 15000 } { 2500 }$

$\sf\longrightarrow \: h = 6 \: m$

Hence ,

• Height is 6 m