Question

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

Answer 1

Answer:

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

Answer:

The answer to your question is 9000 cm^2.

Step-by-step explanation:

Let the common multiple be x.

So, the three sides of the triangle are 12 x, 17 x and 25 x.

Perimeter of the triangle = 540 cm  

Therefore, 12 x + 17 x + 25 x = 540 ( Perimeter property of a triangle)  

54 x = 540

x = 10  

Now as we got the value of x, lets substitute these values into the equations. Therefore,

a = 12 x = 12 x 10 = 120 cm

b = 17 x = 17 x 10 = 170 cm  

c = 25 x = 25 x 10 = 250 cm

s = (a + b + c)/2 =  (120 + 170 + 250)/2 = 540/2

= 270 cm

By using Herons formula,  =  root under (√s(s -a) (s -b)(s -c))

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

=   √(√270 x 150 x 100 x 20)  

=  100√(√27 x 15 x 20)

=  100 x 9 x 5 x 2  

= 9000 cm^2.

Hence, the area is 9000 cm^2.