The sides of a triangle are 8 cm, 12 cm, and 16 cm. What is the area of the triangle?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 12√15.
Given that
The sides of a triangle are 8 cm, 12 cm, and 16 cm
We know that,
The area of triangle ABC = √[s × (s – a) × (s – b) × (s – c)]
where, s = (a + b + c)/2,
a, b, and c are the sides of the triangle
So,
⇒ s = (8 + 12 + 16)/2 = 36/2 = 18 cm
The area of the triangle = √[s × (s – a) × (s – b) × (s – c)]
⇒ √[18 × (18 – 8) × (18 – 12) × (18 – 16)]
⇒ √[18 × 10 × 6 × 2] = √2160 = 12√15 cm2