Question

The perimeter of a triangle field is 270m and its sides are in the ratio 25:17:12:. Find its area

Answer 1

perimeter =270 m

ratio of sides = 25 : 17 : 12

let constant ratio be 'x'

so now sides are 25x m , 17x m, 12x m

sum of all sides(perimeter)= 270 m

25x + 17x + 12x = 270

54x = 270

x = 5

so now , lengths of sides are ,

25x = 25× 5= 125 m

17x = 17 ×5= 85 m

12x = 12 × 5 = 60 m

p = 270

semiperimeter (s) = p /2 = 270/2 = 135 m

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

here , a = 125 m, b = 85 m ,c = 60m,
and s =135

area=√{135(135 -125)(135-85) (135 - 60)}

=√(135×10×50×75)

=√5062500

=2250m^2

therefore , area of triangle = 2250 m^2
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Your Answer : 2250 m^2
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