Question : The sides of a triangle are 8 cm, 12 cm, and 16 cm. What is the area of the triangle?
Option 1: $24 \sqrt{15}~\text{cm}^2$
Option 2: $6 \sqrt{15}~\text{cm}^2$
Option 3: $8 \sqrt{15}~\text{cm}^2$
Option 4: $12 \sqrt{15}~\text{cm}^2$
Correct Answer: $12 \sqrt{15}~\text{cm}^2$
Solution :
The sides of the triangle are 8 cm, 12 cm, and 16 cm.
Semi perimeter = $\frac{8+12+16}{2}$ = 18
Area of the triangle = $\sqrt{18×(18 - 8)×(18 - 12)×(18 -16)}$
= $\sqrt{18×10×6×2}$
= $\sqrt{2160}$
= $12\sqrt{15}\ \text{cm}^2$
Hence, the correct answer is $12\sqrt{15}~\text{cm}^2$.
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