Question

side of triangle are in ratio 12:17:25: and its perimeter is 540. find its area?

Answer 1

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.

Hope it helps u mark as brainliest please

Answer 2

Let, 1st side =12x

2nd side=17x

3rd side=25x

The perimeter of triangle= (12x+17x+25x)

=54x

ATQ,

54x=540

or,x=10

the area is-

$\sqrt{ \frac{120 + 170 + 250}{2}(270 - 120)(270 - 170)(270 - 250) } \\ = \sqrt{270 \times 150 \times 100 \times 20} \\ = 9000 \: {cm}^{2}$