Question : What is the area of a triangle whose sides are of lengths 12 cm, 13 cm and 5 cm?
Option 1: $30 \, \text{cm}^2$
Option 2: $15 \, \text{cm}^2$
Option 3: $40 \, \text{cm}^2$
Option 4: $70 \, \text{cm}^2$
Correct Answer: $30 \, \text{cm}^2$
Solution :
The triangle with sides 12 cm, 13 cm, and 5 cm is a right-angled triangle (since $12^2 + 5^2 = 13^2$).
The area of a right-angled triangle = $\frac{1}{2} \times \text{base} \times \text{height}$.
Here, the base and height are the two shorter sides of the triangle.
The area of the triangle = $\frac{1}{2} \times 12 \, \text{cm} \times 5 \, \text{cm} = 30 \, \text{cm}^2$.
Hence, the correct answer is $30 \, \text{cm}^2$.
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