The sides of a triangle are in the ratio of 2:3:4. If the perimeter of the triangle is 45 CM, find the length of each side of the triangle.

Given: The ratio of sides of triangle  =   2:3:4 

The perimeter of the triangle is 45 cm

To find: The length of each side of the triangle Solution:

Solution:

Lets take the sides of triangles be  $2 x  ,  3 x  ,  4 x$.

$x$ is the proportion between three sides.

Perimeter  =  45 cm.

Perimeter   =  sum of all sides of triangle.

Perimeter   =  $2 x + 3 x + 4 x$                                   [add $2 , 3 , 4 ;  2 + 3+ 4  = 9$]

Perimeter   =   $9 x$

So, compare it with given perimeter,

$9 x   =  45$

$x  =  \frac{45}{9}$  =  5

Substitute  $x = 5 \  in \  2 x , 3 x , 4 x$    

$2 \times(5)  =  10$

$3 \times(5)  =  15$

$4 \times(5)  =  20$

So, sides of triangle are,   10 cm , 15 cm , 20 cm

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Updated on: 10-Oct-2022

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