Question

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

Answer 1

12x + 17x + 25x = 540
x ( 12 + 17 + 25 ) = 540
54x = 540
x = 10
Thus, the sides are
120 cm
170 cm
250 cm

Now you can find the area.

Answer 2

☆ Solution ☆

Given :-

• Sides of a triangle are in ratio 12 17 25 and its perimeter is 540.

To Find :-

• Its area .

Step-by-Step-Explaination

Let side of traingle be 12x, 17x, and 25x

As we know that :-

Perimeter of triangle = a + b + c

So,

a, b and c are sides of triangle

So,

=> 12x + 17x + 25x = 540

=> 54x = 540

=> x = $\dfrac{540}{54}$

=> x = 10

Side will be

=> 12x = 12 × 10 = 120

=> 17x = 17 × 10 = 170

=> 25x = 25 × 10 = 250

Now,

we use heron's formula of area .

As we know that :-

Area of triangle = $\sqrt{s(s - a)(s - b)(s - c)}$

So,

s = $\dfrac{perimeter}{2}$

s = $\dfrac{540}{2}$

s = 270

Semi - perimeter is 270.

Using heron's formula

=> $\sqrt{270(270- 120)(270 - 170)(270- 250)}$

=> $\sqrt{270 \times 150 \times 100 \times 20}$

=> $\sqrt{2 \times 3 \times 3 \times 3 \times 5 \times 2 \times 3 \times 5 \times 5 \times 2 \times 2 \times 5 \times 5 \times 2 \times 2 \times 5}$

=> 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5

=> 9000

Hence,

The area of triangle is 9000.