Question

Q. If perimeter of a triangle is 24cm and sides are in the ration 2:1:3, then find its longest side.​

Answer 1

Answer:

12cm

Step-by-step explanation:

2:1:3 = 6 parts in total

24cm ÷ 6 = 4cm per part

The longest side is 3 parts:

4cm x 3 = 12cm

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You could also realise that 3 parts are half of 6parts

And do ²⁴⁄₂ = 12cm

Answer 2

Answer :-

• The longest side of the triangle is 12 cm.

To find :-

• The length of the longest side of the triangle.

Solution :-

• Before finding the length of the longest side of the triangle, let's find the length of all it's sides!

Let :-

• The sides of the triangle be 2x, x and 3x, as they are in the ratio 2 : 1 : 3.

We know that :-

$\underline{ \boxed{ \sf Perimeter \: of \: a \: triangle = Sum \: of \: all \: sides}}$

Here,

• The sides are 2x, x and 3x.
• The perimeter is 24 cm.

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Therefore,

$\implies \rm2x + x + 3x = 24$

$\implies\rm6x = 24$

$\implies \rm x = \dfrac{24}{6}$

$\implies\overline{ \boxed{\rm x = 4 \: cm}}$

Hence, the sides of the triangle are :-

$\bf2x = 2 \times 4 = 8 \: cm.$

$\bf x = 4 \: cm.$

$\bf3x = 3 \times 4 = 12 \: cm.$

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Now, we see that :-

• 12 cm is the largest number here.

Hence :-

• The longest side of the triangle is 12 cm.