Question

The ratio of the sides of triangle 4:3:2.
The perimeter of the triangle is 108 cm,
What is the length of the longest side?​

Answer 1

$\huge\underline\mathfrak{Question-}$

The ratio of the sides of triangle 4:3:2.

The perimeter of the triangle is 108 cm,

What is the length of the longest side?

$\huge\underline\mathfrak{Answer-}$

Length of the longest side is 48cm.

$\huge\underline\mathfrak{Explanation-}$

Let, AB = 2x, AC = 3x and BC = 4x

It is given that, perimeter of ∆ABC = 108 cm

$\large{\boxed{\boxed{\red{\mathrm{Perimeter\:of\:triangle=AB+BC+CA}}}}}$

$\mapsto$ 108 = 2x + 4x + 3x

$\mapsto$ 108 = 9x

$\mapsto$ x = $\rm{\cancel{\dfrac{108}{9}}}$

$\mapsto$ $\large{\boxed{\mathrm{x=12}}}$

$\rule{200}1$

★ Length of longest side :

$\mapsto$ BC = 4x

Put x = 12

$\mapsto$ BC = 4 × 12

$\mapsto$ BC = 48 cm

Hence, the length of longest side is 48 cm.

Answer 2

Answer:

Length of longest side = 48 cm

Step-by-step explanation:

We Have :-

Ratio of sides of triangle = 4:3:2

Perimeter of triangle = 108 cm

To Find :-

Length of the longest side of Triangle

Solution :-

Let the sides of the triangle be 4x , 3x , 2x

Perimeter of Triangle = Side + Side + Side

108 = 4x + 3x + 2x

108 = 9x

x = 12

Sides of triangle are :-

4x = 4 * 12 = 48 cm

3x = 3 * 12 = 36 cm

2x = 2 * 12 = 24 cm

Length of longest side = 48 cm