Question : The inradius of a triangle is 6 cm, and the sum of the lengths of its sides is 50 cm. The area of the triangle (in sq. cm) is:
Option 1: 150
Option 2: 50
Option 3: 300
Option 4: 56
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Correct Answer: 150
Solution :
The area of a triangle by using the formula involving the inradius ($r$) and the semi-perimeter ($s$) of the triangle.
$\text{Area} = rs$
Given that the inradius is 6 cm, the sum of the lengths of its sides is 50 cm, and the semi-perimeter is 25 cm.
$\text{Area} = r \times s = 6 \, \text{cm} \times 25 \, \text{cm} = 150 \, \text{sq. cm}$
Hence, the correct answer is 150.
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