Question

Cube root of the perimeter of a triangular field us 7m and its sides are in the ratio 14:15:20. Find the area of the triangle

Answer 1

GIVEN : The perimeter of a triangular field = 7^3m
=343m

Let the sides are 14x , 15x , 20 x
[Since the sides are in the ratio 14:15:20,we can assume sides as 14x,15x,20x. It is applicable in every case were ratios involved].

Perimeter of a ∆ = sum of three sides

14x + 15x + 20x = 343m

49x = 343

x = 343/49=49/7=7

1st side (a) = 14x = 14×7= 98m

2nd side(b)= 15x = 15×7= 105m

3rd side (c)= 20x = 20× 7 =140m



Area of the ∆= √ S(S - a)(S - b)(S - c)
where,
a,b,c are the sides and
S=(a+b+c)/2

[By Heron’s Formula]
s=140+105+98/2 =343/2
=171.5

Area,A= √ S(S - 98)(S - 105)(S - 140)

= √ 171.5(171.5 - 98)(171.5- 105)(171.5 - 140)

= √ 171.5×73.5×66.5×31.5

= 2016283 m^2

Area of the ∆= 2016283 m²