Question

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

Answer 1

Given :-

Sides of a triangle are in the ratio = 12 : 17 : 25

Perimeter of the triangle = 540 cm

To Find :-

Area of the triangle.

Analysis :-

First consider the common ratio as a variable.

Make an equation accordingly at finally find the sides by substituting the value of the variable you get.

Next find the semi perimeter of the triangle accordingly.

Once you get the semi perimeter, find the area by the Heron's formula.

Solution :-

We know that,

• a = Area
• s = Semi perimeter

Consider the common ratio as 'x'. Then the sides would be 12x, 17x and 25x.

Given that,

Perimeter of the triangle = 540 cm

Making an equation,

12x + 17x + 25x = 540

54x = 540

Finding x,

x = 540/54

x = 10 cm

The sides would be,

12x = 12 × 10 = 120 cm

17x = 17 × 10 = 170 cm

25x = 25 × 10 = 250 cm

Finding semi perimeter,

$\sf \dfrac{540}{2} =270 \ cm$

Using Heron's formula,

$\underline{\boxed{\sf Heron's \ formula=\sqrt{s(s-a)(s-b)(s-c)} }}$

Substituting their values,

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

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

$\sf =\sqrt{81000000 }$

$\sf =9000 \ cm^2$

Therefore, the area of the triangle is 9000 cm².