Question

19 the sides of a triangle are in the ratio of 2: 3: 4 if perimeter is 72 cm, find its sides​

Answer 1

Answer :-

The sides of the triangle are :-

• 16cm
• 24cm
• 32cm.

Step-by-step explanation :

To Find :-

• The sides of triangle

Solution :-

Given that,

• Perimeter of triangle = 72cm
• The sides of a triangle are in the ratio of = 2:3:4

As we know that,

Perimeter of triangle = Sum of all sides,

Assumption:

Let us assume the unknown sides of triangle as 2x, 3x and 4x,

Therefore,

• 2x + 3x + 4x = 72

=> 2x + 3x + 4x = 72

=> 5x + 4x = 72

=> 9x = 72

=> x = 72/9

=> x = 8

• The value of x is 8.

Now, the sides are :-

• The side which we assumed as 2x

=> 2x

=> 2*8

=> 16cm

• The side which we assumed as 3x

=> 3x

=> 3*8

=> 24cm

• The side which we assumed as 4x

=> 4x

=> 4*8

=> 32cm

Hence,

The sides of the triangle are :-

• 16cm
• 24cm
• 32cm.

Answer 2

Given:

A triangle with

• Ratio of sides = 2 : 3 : 4
• Perimeter = 72 cm

What To Do:

We have to find the sides of the triangle.

How To Do:

To find the sides of the triangle, we have to

• Take x as the common multiple in the ratio 2 : 3 : 4 = 2x : 3x : 4x
• Take sum of all three sides to find the perimeter of triangle.
• Form the equation as 2x + 3x + 4x = 72 cm and solve it.

Solution:

2x + 3x + 4x = 72 cm

Add the terms in LHS,

⇒ 9x = 72 cm

Take 9 to RHS,

⇒ x = $\dfrac{72}{9}$

Divide 72 by 9,

⇒ x = 8

Now, substitute the values,

• 2x = 2 × 8 = 16 cm
• 3x = 3 × 8 = 24 cm
• 4x = 4 × 8 = 32 cm

∴ Therefore, the sides of the triangle are 16 cm, 24 cm and 32 cm respectively.