Question

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

Answer 1

∴ Sides of triangle will be: 12x,17x and 25x

⇒Perimeter =540 cm(given)

⇒12x+17x+25x=540 cm,

⇒54x=540 cm

⇒x=10 cm

∴ Sides of triangle: a=120,b=170,c=250 cms

⇒2S=540

⇒S=270 cm

A= s(s−a)(s−b)(s−c)

= 270(270−120)(270−170)(270−250)

= 270×150×100×20

A=9000 cm²

Answer 2

Answer :-

• Area of Triangle = 9000 sq.cm.

Explanation :-

Given :

• Sides are in ratio 12 : 17 : 25.

• Perimeter of Triangle = 540 cm.

To Find :

• Area of Triangle.

Solution :

Let the sides be 12x, 17x and 25x.

And, We know that,

Perimeter of Triangle = Sum of all sides.

So, Put the values.

⇒ 12x + 17x + 25x = 540 cm.

⇒ 29x + 25x = 540 cm.

⇒ 54x = 540 cm.

⇒ x = 10 cm.

Therefore,

• 12x = 120 cm.
• 17x = 170 cm.
• 25x = 250 cm.

Now, Let's Calculate Area.

We will use Heron's Formula here.

First, Let's Calculate Semi-Perimeter.

s = (a + b + c)/2.

Here,

• s = Semi Perimeter.
• a = First side.
• b = Second Side.
• c = Third Side.

Put the values.

⇒ s = (120 + 170 + 250)/2.

⇒ s = 540/2.

⇒ s = 270 cm.

Now, Let's use Heron's Formula.

Heron's Formula = √s(s − a)(s − b)(s − c).

Put the values.

⇒ Area = √270(270−120)(270−170)(270−250)

⇒ Area = √270 × 150 × 100 × 20.

⇒ Area = √81000000.

⇒ Area = 9000 sq.cm.

Therefore, Area of Triangle = 9000 sq.cm.