A triangular field has side lengths in the ratio 2 : 3 : 4 and perimeter 72 m. What is the area?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 186 m2.
Let the sides be 2k, 3k, and 4k
Perimeter = 2k + 3k + 4k = 9k = 72
⇒ k = 8
Sides are 16 m, 24 m, and 32 m
Semiperimeter (s) = (16 + 24 + 32)/2 = 72/2 = 36
Area = √[36 × (36–16) × (36–24) × (36–32)]
= √[36 × 20 × 12 × 4]
= √34560
≈ 186 m2