Question

1.The sides of a triangle are in the ratio 12:17:25 and its perimeter is 540 cm. Find its area by using heron's formula
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Answer 1

Answer:

Let common ratio be x

Sum of sides = perimeter

12x + 17x + 25x = 540cm

54x = 540cm

x = 540/54

x=10

12x = 12*10 = 120cm

17x = 17*10 =  170cm

25x = 25*10 = 250cm

To find area:

s= 540/2 = 270

Area = root s(s-a)(s-b)(s-c)

= root 270*150*100*20 = root 81000000

= 9000 cm^2

Answer 2

Answer:

9000

Step-by-step explanation:

Let the ratios be n,

A/Q,

12n+17n+25n = 540

54n = 540

n = 10

first side = a = 120cm

second side = b = 170cm

third side = c = 250cm

s = a/2 +b/2 +c/2

= 60cm + 85cm + 125cm

= 270cm

Area = $\sqrt{s(s-a)(s-b)(s-c)$

= $\sqrt{270(270-120)(270-170)(270-250)$

=$\sqrt{270(150)(100)(20)}$

=√81000000

= 9000