1. **Problem statement:** We have a rectangular hall with a floor perimeter of 250 m. The cost of painting the four walls is 15000 at a rate of 10 per m². We need to find the height of the hall. 2. **Known values:** - Perimeter of floor, $P = 250$ m - Cost of painting, $C = 15000$ - Rate of painting per m², $r = 10$ 3. **Formulas and concepts:** - Perimeter of rectangle: $$P = 2(l + w)$$ where $l$ is length and $w$ is width. - Area of four walls (lateral surface area): $$A = 2h(l + w)$$ where $h$ is height. - Cost of painting: $$C = r \times A$$ 4. **Step 1: Find $l + w$ from perimeter:** $$250 = 2(l + w) \implies l + w = \frac{250}{2} = 125$$ 5. **Step 2: Find area of four walls using cost and rate:** $$C = r \times A \implies A = \frac{C}{r} = \frac{15000}{10} = 1500 \text{ m}^2$$ 6. **Step 3: Use area formula to find height $h$:** $$A = 2h(l + w) \implies 1500 = 2h \times 125$$ $$1500 = 250h \implies h = \frac{1500}{250} = 6$$ **Final answer:** The height of the hall is $6$ meters.