Question

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

Answer 1

Question :-

The sides of a triangle are in the ratio 12:17:25 and it's perimeter is 540cm find its area

Answer :-

Area of the Triangle ↬ 9000 cm²

Given :-

• Ratio of sides = 12:17:25
• Perimeter of triangle = 540 cm

Have to Find :-

• Area of the Triangle

Solution :-

Let's consider the sides of the triangle be 12x , 17x and 25x .

So , now According to the Question :-

a + b + c = 540

Then ,

12x + 17x + 25x = 540 cm

⇒ 54x = 540 cm

⇒ x = 10 cm

Therefore , the sides of triangle be :-

↬ a = 12x = 12 × 10 = 120cm

↬ b = 17x = 17 × 10 = 170cm

↬ c = 25x = 25 × 20 = 250cm

So , Now

↬ 2S = 540 [ Half Perimeter ]

↬ S=270 cm

We know the herons formula :-

A = √s (s−a) (s−b) (s−c)

Then , the area is

Area = √270 (270−120) (270−170) (270−250)cm ²

= √270 × 150 × 100 × 20cm²

Hence ,

$Area$ = 9000 cm²

Answer 2

☆ Solution ☆

Given :-

• The sides of a triangle are in the ratio 12:17:25 and it's perimeter is 540 cm.

To Find :-

• Its area .

Step-by-Step-Explaination

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

Perimeter = 540 cm

⇒ 12x + 17x + 25x = 540

⇒ 54x = 540

⇒ x = 540/54

⇒ x = 10

a = 12 × 10 = 120 cm

b = 17 × 10 = 170 cm

c = 25 × 10 = 250 cm

Now,

$s = \dfrac{a + b + c}{2}$

$s = \dfrac{540}{2}$ = 270

As we know that :-

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

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

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

$\sqrt{81000000}$

9000 cm²