Question

The perimeter of a triangular field is 540 m and its side are in the retio 25:17:12 find the area of the triangle. also find the cost of ploughing the field at Rs 18. 80 per 10m2

Answer 1

ratio of sides 25X :17X:12X(let)
so
25X+17X+12X=540
54X=540
X=10
3 sides are25*10=250
17*10=170
12*10=120
semi perimeter= 540/2=270
area =[s(s-a)(s-b)(s-c)
=[270(270-250)(270-170)(270-120)
=[270*20*100*150
=[81000000
=9000
10 m2=18.80
1 m2=1.88
9000m2=9000*1.88=88920

Answer 2

if the sides are 25x , 17x , 12x where x is any positive no. then 

25x + 17x + 12x = 540 
54x = 540 

x = 10 

then the sides are 250m , 170m & 120m. 
the semi - perimeter is S = 540/2 = 270 m 

now the area of the triangle is 
= √ S*(S - 250)*(S - 170)*(S - 120) sq. m 

= √ 270*(270 - 250)*(270 - 170)*(270 - 120) sq. m 

= √ 270*20*100*150 sq. m 

= √ 81000000 sq.m 

= 9000 sq.m
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