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------------------------------------------------ The length and breadth of an auditorium are in the ratio 3:2. If the area of the ceiling is 600 sq. m and the area of four walls is 1500 sq. m, then the height of the auditorium is:

a) 20 meters
b) 30 meters
c) 40 meters
d) 50 meters

Answer :

The height of the auditorium is 30 meters. The correct answer is option B.

Given:

- The length and breadth of the auditorium are in the ratio 3:2.

- The area of the ceiling is 600 sq. m.

- The area of the four walls is 1500 sq. m.

Step 1: Calculate the length and breadth of the auditorium.

Let the length be 3x and the breadth be 2x, where x is a constant.

Area of the ceiling = 3x × 2x = 6x²

600 = 6x²

x = 5 meters

Length = 3x = 3 × 5 = 15 meters

Breadth = 2x = 2 × 5 = 10 meters

Step 2: Calculate the height of the auditorium.

Area of the four walls = 2(15 × 30) + 2(10 × 30) = 1500 sq. m

Height = 1500 / (2 × (15 + 10)) = 30 meters

Therefore, the height of the auditorium is 30 meters.

The correct answer is option B.

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