Question

the sides of a triangle are in the ratio 4:5:6.The perimeter of a triangle id 45cm.Find the sides of the triangle.​

Answer 1

Question given :

• the sides of a triangle are in the ratio 4:5:6.The perimeter of a triangle id 45cm.Find the sides of the triangle.

Given :

• The sides of a triangle are in ratio 4:5:6
• The perimeter of the traingle is 45 cm

To find :

• The length of all three sides

Formula used :

• Perimeter of a triangle = Side + Side + Side

Solution :

Let the three sides be 4x , 5x and 6x respectively .

Now by using the formula to find the perimeter we have ,

= 4x + 5x + 6x = 45 cm

= 15x = 45 cm

= x = $\sf\dfrac{45}{15}$

= x = 3 cm

Length of side 1 = 4x

= 4 × 3 = 12 cm

Length of side 2 = 5x

= 5 × 3 = 15 cm

Length of side 3 = 6x

= 6 × 3 = 18 cm

Verification :

= Perimeter = Sum of all three sides

= Perimeter = 12 + 15 + 18 cm

= 45 cm = 45 cm

= LHS = RHS

Hence verified that the sides measure as 12 , 15 and 18 cm respectively

Answer 2

Answer

$\red{\bigstar}$ The sides of triangle $\leadsto$

• First side $\leadsto$ ${\boxed{\sf{\red{12~cm}}}}$
• Second side $\leadsto$ ${\boxed{\sf{\red{15~cm}}}}$
• Third side $\leadsto$ ${\boxed{\sf{\red{18~cm}}}}$

• Given

• Ratio of sides of triangle = 4 : 5 : 6
• Perimeter of triangle = 45 cm

• To find

• Sides of triangle

• Solution

Let the sides of triangle be 4x, 5x and 6x.

$\purple{\bigstar}$ $\boxed{\underline{\sf{Perimeter = Sum~of~all~sides}}}$

Substitute the given values,

⟶ 4x + 5x + 6x = 45

⟶ 15x = 45

⟶ x = 45/15

⟶ x = 3

The value of x = 3.

The three sides of triangle -

• First side = 4x = 4 × 3 = 12 cm
• Second side = 5x = 5 × 3 = 15 cm
• Third side = 6x = 6 × 3 = 18 cm

____________________________________

Let's verify -

$\purple{\bigstar}$ $\boxed{\underline{\sf{Perimeter = Sum~of~all~sides}}}$

Perimeter of triangle = 45 cm

The three sides of triangle $\leadsto$ 12 cm, 15 cm, 18 cm.

Their sum ⟶

⟶ 12 + 15 + 18

⟶ 45

$\purple{\bigstar}$ Hence, verified.