Question

The sides of a triangle are in ratio 25:17:12 and its perimeter is 540m. Find the area of the triangle

Answer 1

$25x + 17x + 12x = 540 \\ 54x = 450 \\ x = \frac{540}{54} \\ x = 10 \\ \\ so.(25 \times 10).(17 \times 10).(12 \times 10) \\ \\ hence.250.170.120$

Answer 2

Here is your solution

GIVEN:-

perimeter = 540m

sides are in ratio 25:17:12

The sides are 25x , 17x , 12x where x is any positive no. 

Now

25x + 17x + 12x = 540 

54x = 540 

x = 10 

25x = 25 * 10 = 250

17x = 17*10 = 170

12x = 12*10 = 120

So, the sides are 250m , 170m & 120m. 

now, the semi - perimeter is S = 540/2 = 270 m

we know the Heron's formula:-

$= \sqrt{s(s - a)(s - b)(s - c)}  \\  =  \sqrt{270(270 -250 )(270 -17 )(270 -120 }  \\  =  \sqrt{270×20 × 100 × 150}  \\   = \sqrt{810000}  \\  = 9000m {}^{2}$

Hence area of triangle is 9000m^2

hope it helps you