Question

The sides of a triangle are in the ratio 3:5:7. If its perimeter is 45 cm, find the length of each side.​

Answer 1

Given :-

Ratio of sides of triangle - 3 : 5 : 7

Perimeter - 45

To Find :-

Length of each side

Solution

Let the side be = x

So,

3x + 5x + 7x = 45  (As perimeter is equal to sum of all sides)

15x = 45

x = 45/15

x = 3

Finding length of each side :-

3 x 3 = 9cm

5 x 3 = 15cm

7 x 3 = 21cm

Verification

9 + 15 + 21 = 45

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The sides of the triangle are 9 cm, 15 cm and 21 cm.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Ratio of the sides of the triangle = 3 : 5 : 7

Perimeter of the Triangle = 45 cm

To Find :

The length of each side.

Solution :

Consider -

• One side as 3x
• Second side as 5x
• Third side as 7x

The given Triangle is a Scalene triangle, that means it's all sides are of different Measures.

★ Perimeter = $\boxed{\sf{Side+Side+Side}}$

$\longrightarrow$ 3x + 5x + 7x = 45

$\longrightarrow$ 10x + 5x = 45

$\longrightarrow$ 15x = 45

$\longrightarrow$ x = 45/15

$\longrightarrow$ x = 3

$\rule{300}{1.5}$

★ $\textbf{\small{\underline{Value of 3x}}}$

$\longrightarrow$ 3 × 3

$\longrightarrow$ 9

$\rule{300}{1.5}$

★ $\textbf{\small{\underline{Value of 5x}}}$

$\longrightarrow$ 5 × 3

$\longrightarrow$ 15

$\rule{300}{1.5}$

★ $\textbf{\small{\underline{Value of 7x}}}$

$\longrightarrow$ 7 × 3

$\longrightarrow$ 21

$\therefore$ The sides of the triangle are 9 cm, 15 cm and 21 cm.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\longrightarrow$ 9 + 15 + 21 = 45

$\longrightarrow$ 24 + 21 = 45

$\longrightarrow$ 45 = 45

$\therefore$ The sides of the triangle are 9 cm, 15 cm and 21 cm.