Question

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

Answer 1

Answer:-

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 → h = 6

Therefore, the height of the hall is 6 m.

Answer 2

$\bigstar$ Given:

• Perimeter of the floor of a rectangular hall = 250 m
• Cost of painting per square meter area = Rs.10
• Cost of painting the four walls = Rs. 15000 (Rs. 10 per $m^{2}$)

$\bigstar$ To Find:

• Find the height of the hall.

$\bigstar$ Solution:

Let us consider length, breadth, and height of the rectangular hall as l, b, and h respectively.

According to the question,

Area of four walls = $2lh + 2 bh$

$\implies 2 (l + b) h$

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

$\implies 250 \: m$

Area of four walls = $2(l + b) h = 250h \: m^{2}$

Given, cost of painting per square meter area = Rs.10

∴ Cost of painting 250h square meter area = $Rs. \: (250 h \times 10) = Rs. \: 2500h$

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.