Discussion

The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 300 m, its area is?

Answer: A

Write the sides as multiples of a common factor and use the perimeter.

\[ 5k + 12k + 13k = 300 \quad\Longrightarrow\quad 30k = 300 \quad\Longrightarrow\quad k = 10 \]

\[ \text{sides} = 50,\; 120,\; 130 \text{ m} \]

Since \( 5^{2} + 12^{2} = 13^{2} \), the triangle is right-angled with the two shorter sides as legs:

\[ A = \frac{1}{2} \times 50 \times 120 = 3000 \text{ m}^{2} \]

Recognising the 5–12–13 triple avoids Heron's formula entirely.

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