Discussion
If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
Answer: A
Check the sides first: \( 10^{2} + 24^{2} = 100 + 576 = 676 = 26^{2} \), so this is a right-angled triangle with legs 10 cm and 24 cm.
\[ A = \frac{1}{2} \times 10 \times 24 = 120 \text{ cm}^{2} \]
Heron's formula agrees: with \( s = 30 \), \( \sqrt{30 \times 4 \times 6 \times 20} = \sqrt{14400} = 120 \). Spotting the 5–12–13 triple doubled saves that work.
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