Question

sides of a triangle are in ratio 12:17:25 and it's perimeter is 540cm. find it's area​

Answer 1

Answer:

here is your answer mate

Step-by-step explanation:

ratio of sides  = 12: 17:25

let them be  =

12x,17x, 25x respectively

perimeter of a triangle = sum of all sides

540 = 12x,17x, 25x

540 = 54x

x = 10

all sides measure

12x = 12×10 = 120

17x = 17× 10 = 170

25x= 25 × 10 = 250

it's semipetimeter = 540/2

= 270

using heron's formula area of the triangle =

root {(s)(s-a)(s-b)(s-c)}

where s is the semipetimeter and a,b,c

area the sides of the triangle.

root {( 270)(270-120)(270-170)(270-250)}

= 9000cm^2.

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