UPSC CAPF Assistant Commandant Model Paper 5

GIVEN:
Sides of triangular field = 18 m, 80 m and 82 m
CONCEPT:
area of a triangular park = 5√3 × the area of a triangular field
FORMULAE USED:
Area of an equilateral triangle = (√3/4) a2
Area of triangle with sides a, b, and c = √[s(s - a)(s - b)(s - c)], where s = (a + b + c)/2
CALCULATION:
s = (18 + 80 + 82)/2 = 90
The area of a triangular field = √[90(90 - 18)(90 - 80)(90 - 82)] = √[90 × 72 × 10 × 8] =720 m2
According to question,
(√3/4) a2 = 5√3 × 720
a = 120
∴ side of the triangular park = 120 m