Question

The sides of a triangular field are in the ratio 13 ∶ 14 ∶ 15 and its perimeter is 840 m. The area of the field, in hectares is:
1. 3.42
2. 3.36
3. 3.12
4. 3.24

Answer 1

Correct Answer - Option 2 : 3.36

FORMULAE USED:

Area of the triangle = √{s(s - a)(s - b)(s - c)}

CALCULATION:

Let sides of triangle is 13x, 14x, and 15x.

According to the question

13x + 14x + 15x = 840

42x = 840

x = 20 

Now,

s = (13x + 14x + 15x)/2 = 420

a = 13 × 20 = 260

b = 14 × 20 = 280

c = 15 × 20 = 300

Area of the triangle = √{420(420 - 260)(420 - 280)(420 - 300)}

Area of the triangle = √{420 × 160 × 140 × 120} = 2400 m2

= 33600 m²

= 3.36 square hectare

Hence, 3.36 is the correct answer.