Discussion
A triangular ground has 8km, 10km and 6km as its sides. It is to be painted at the rate of Rs. 8 per sq.km. How much will it cost?
Answer: D
Check the sides first - \( 6^{2} + 8^{2} = 36 + 64 = 100 = 10^{2} \), so this is a right-angled triangle with legs 6 km and 8 km.
\[ A = \frac{1}{2} \times 6 \times 8 = 24 \text{ km}^{2} \]
\[ \text{cost} = 24 \times 8 = \text{Rs. } 192 \]
Heron's formula gives the same result: with \( s = 12 \), \( \sqrt{12 \times 4 \times 2 \times 6} = \sqrt{576} = 24 \). Spotting the Pythagorean triple simply saves the work.
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