Question

Chapter: Herons' formula
4. Sides of a triangle are in the ratio 12:17:25 and its perimeter is 540cm. Find its area.

Answer 1

Area of traingle=√s(s-a)(s-b)(s-c)
here, s is the semi perimeter,
and A,B,C are sides of a triangle

Given perimeter=540cm

semi perimeter=s=perimeter/2

s=540/2
s=270

let sides be a=12xcm,b=17xcm,c=25xcm

now,
perimeter=540
a+b+c=540

12x+17x+25x=540
54x=540
x=540/54
x=10


so, a=12x, =12×10=120
b=17x =17×10=170
c=25x =25×10=250

area=√270(270-120)(270-170)(270-250)
=√270×150×100×20
=√(27×15×2)×(10)5
=√(27×30)×(10)5
=√(27×3)×(10)6
=√(81)×(10)6
=√81×√(10)6
= 9× (10)3
=9×1000
=9000
thus, area=9000cm2

Answer 2

Given :-

Sides of a triangles are in the ratio of 12:17:25 and it's perimeter is 540cm.

To Find :-

Area

Solution :-

Let the sides be 12x, 17x and 25x

Perimeter = a + b + c

540 = 12x + 17x + 25x

540 = 54x

540/54 = x

10 = x

Therefore

Sides are

12x = 12(10) = 120 cm

17x = 17(10) = 170 cm

25x = 25(10) = 250 cm

Now

Semiperimeter = Perimeter/2

Semiperimeter = 540/2

Semiperimeter = 270 cm

Now

Area = √s(s - a)(s - b)(s - c)

Area = √270(270 - 120)(270 - 170)(270 - 250)

Area = √270 × 150 × 100 × 20

Area = √(8,10,00,000)

Area = 9000 cm²

Therefore

Area of triangle is 9000 cm²