Question

The sides of a triangle are in the ratio 2:3:5, if its Perimeter is
100cm, the length of the smallest side is
a) 2 cm
b) 20cm
c) 3 cm
d) 5cm
​

Answer 1

Step-by-step explanation:

Let sides be 2x , 3x , 5x

Perimeter of triangle = 100

2x + 3x + 5x = 100

10x = 100

x = 10

Smallest side = 2x = 20 cm Ans....

Answer 2

★ Given:

The sides of a triangle are in the ratio 2:3:5.

The perimeter of the triangle is 100 cm.

★ To Find:

The length of the smallest side of the triangle.

★ Analysis

In this question, we will have to change the ratios to terms be applying the variable x. Then we can find the value of x and multiply the required constant of the smallest side to get the answer.

★ Solution:

Let the three sides of the triangle be 2x, 3x and 5x.

Perimeter of the triangle = 100 cm

Forming an equation:

2x + 3x + 5x = 100 cm

10x = 100 cm

So x = 100/10

x = 10

Among the given terms, 2x is the smallest so 2x will be the measure of the smallest side of the triangle.

Measure of the smallest side = 2x

= 2 x 10

= 20 cm

★ Verification:

We can first the measures of all the sides of the triangles. If we get the perimeter as given in the question, our answer is correct.

2x = 2 x 10 = 20 cm

3x = 3 x 10 = 30 cm

5x = 5 x 10 = 50 cm

Sum of all the sides:

20 + 30 + 50 = 100 cm

Hence Verified!