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

Let the common ratio between the sides of the given triangle be x.

Therefore, the side of the triangle will be 12x, 17x, and 25x.

Perimeter of this triangle = 540 cm

12x + 17x + 25x = 540 cm

54x = 540 cm

x = 10 cm

Sides of the triangle will be 120 cm, 170 cm, and 250 cm.

`s="perimeter of triangle"/2=540/2=270cm`

By Heron's formula,

`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`

`=[sqrt(270(270-120)(270-170)(270-250))]cm^2`

`=[sqrt(270xx150xx100xx20)]cm^2`

= 9000 cm2

Therefore, the area of this triangle is 9000 cm2.

Last updated at Sept. 22, 2017 by

Ex 12.1, 5 Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540 cm. Find its area. Area of triangle = (s(s a)(s b)(s c)) Here, s is the semi-perimeter, and a, b, c are the sides of the triangle Given Perimeter = 540 cm Semi-Perimeter = s = Perimeter/2 s = 540/2 s = 270 cm Given Ratio of sides is 12 : 17 : 25 Let sides be a = 12x cm ,b = 17x cm , c = 25x cm where x is any number Now, Perimeter = 540 cm a + b + c = 540 12x + 17x + 25x = 540 29x + 25x = 540 54x = 540 x = 540/54 x = 10 So, a = 12x cm b = 17x cm c = 25x cm Area of triangle = ( ( )( )( )) Putting a =120 cm, b = 170 cm, c = 250 cm & s = 270 cm Area = (270(270 120)(270 170)(270 250)) cm2 = (270 150 100 20) m2 = ( (27 15 2) (10)5) = ( (27 30) (10)5) = ( (27 3) (10)6) = ( (81) (10)6) = 81 ((10)6) = 92 ((10)6) = (9) (106) ^(1/2) = (9) (103) = 9000 Thus, Area = 9000 cm2

Solution:

Given: Ratio of sides of the triangle and its perimeter.

By using Heron’s formula, we can calculate the area of a triangle.

Heron's formula for the area of a triangle is: Area = √s(s - a)(s - b)(s - c)

Where a, b, and c are the sides of the triangle, and s = Semi-perimeter = Half the perimeter of the triangle

Since the ratios of the sides of the triangle are given as 12:17:25

So, we can assume the length of the sides of the triangle as 12x cm, 17x cm, and 25x cm.

So the perimeter of the triangle will be

Perimeter = 12x + 17x + 25x

12x + 17x + 25x = 540 (given)

54x = 540

x = 540/54