Question

. The sides of a triangle are in the ratio 3:4:5, what is the length of its longest side if the
perimeter is 60 cm.
a) 30 cm
b) 20 cm
c) 24 cm
d) 25 cm​

Answer 1

Given :-

• Ratio is 3:4:5
• And its perimeter is 60 cm

To find :

• Longest side of the triangle

According to the question,

Let the ratio be 3x,4x and 5x

And the perimeter is 60 cm

We know,

⇒ Perimeter of triangle = Sum of all its side

⇒ 60 = 3x + 4x + 5x

⇒ 60 = 12x

⇒ 60 ÷ 12 = x

⇒ 5 = x

Therefore,the value of x is 5.

★ Value of 3x :

⇒ 3x

⇒ 3(5)

⇒ 15 cm

★ Value of 4x :

⇒ 4x

⇒ 4(5)

⇒ 20 cm

★ Value of 5x :

⇒ 5x

⇒ 5(5)

⇒ 25 cm

So,the longest side is 25 cm..

.°. Option D) 25 cm is correct.

______________________________

Answer 2

Given :-

• Ratio of Sides = 3:4:5
• Perimeter = 60 cm

To Find :-

• Length of longest side

Solution :-

Let the measure of 1st side of the traingle be 3x

Let the measure of 2nd side of the traingle be 4x

Let the measure of 3rd side of the triangle be 5x

We know sum of all sides is the perimeter

➥ 3x + 4x + 5x = 60

➥ 3x + 9x = 60

➥ 12x = 60

➥ x = 60/12

➥ x = 5

So, we will simply find the three sides

Measure of 1st side = 3x = 3 × 5 = 15 cm

Measure of 2nd side = 4x = 4 × 5 = 20 cm

Measure of 3rd side = 5x = 5 × 5 = 25 cm

So, the longest side is 3rd side which is 25 cm

So, option (d) 25 cm