Painting four walls – find hall height from cost and perimeter: A rectangular hall has floor perimeter 250 m. Painting the four walls costs ₹ 15000 at ₹ 10 per m^2. Neglect openings and find the height of the hall.

Introduction / Context:
Painting the four walls covers the lateral surface area of the room: area = perimeter of floor × height. Given cost and rate, we can recover area, then divide by perimeter to find height. This is a practical application of unit rates and surface area of prisms.

Given Data / Assumptions:

• Perimeter P = 250 m
• Cost = ₹ 15000
• Rate = ₹ 10 per m^2 → painted area A = 15000 / 10 = 1500 m^2
• A = P × h

Concept / Approach:
Use the formula for the lateral area of a rectangular prism (room without ceiling/floor): it equals the floor perimeter multiplied by wall height. Solve h = A / P.

Step-by-Step Solution:
A = 15000 / 10 = 1500 m^2h = A / P = 1500 / 250 = 6 m

Verification / Alternative check:
If L + W = 125 m (since 2(L + W) = 250), then total wall area = 2h(L + W) * 2? (equivalently P * h) = 250h → with h = 6, area = 1500 m^2; cost = 1500 * 10 = ₹ 15000, consistent.

Why Other Options Are Wrong:
Heights 5, 7, 8, 9 m would give painted areas 1250, 1750, 2000, 2250 m^2 respectively, not matching the billed area of 1500 m^2.

Common Pitfalls:
Attempting to use room length/width individually (they are unnecessary); forgetting that ceilings/floors are excluded in “four walls only.”

Final Answer:
6 m