Question

Sides of a triangles are in the ratio of 12:17
:50 and it's perimeter is 540cm. Find it's area using heron's formula.

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Answer 1

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

Answer 2

Answer:

Let x be common ratio

Sides of triangle is 12x,17x,25x

Perimeter =540cm

12x+17x+25x=540

54=540

x=10cm

Sides of triangle is a=120,b=170,c=250 cms

2s=540cm

s=270cms .

by using herons formula

A=s quare root of s (s-a)(s-b)(s-c)

A=square root of 270 (270-120)(270-170)(270-250)

A= 9000cm square .

Hope it helps u mate

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