Question

12) The sides of atriangles are in the ratio
tu 1:3:5. What is the perimeter of the
length of the lenger side is 15 cm​

Answer 1

Perimeter is the length of the given figure.

For Triangle, It can be defined as the sum of the three sides.

In the question,

Given data

The longest side is 15 cm.

The sides are in the ratio of 3 : 4 : 5

Solution :

Find which value of the ratio is greatest

Given ratio is 3 : 4 : 5

So, Here 5 is the greatest value.

Find the sum of terms in the ratio

3 + 4 + 5 = 12

Now Each side will the fraction of its value in the ratio by sum of ratios multiplied by some factor k

Longest side

⇒5/12 * k = 15

⇒5k = 180

⇒k = 36.

Now, Other two sides are

Side 1 : 3/12 * 36 = 3 * 3 = 9

Side 2 : 4/12 * 36 = 4 * 3 = 12

Side 3 : 5/12 * 36 = 5 * 3 = 15

Now,

Perimeter of triangle = Side 1 + Side 2 + Side 3

So, Perimeter = 9 + 12 + 15 = 36

Therefore, Perimeter of the given triangle is 36 cm.

Answer 2

Answer:

Given: Ratio of Sides = 12: 14: 25

Perimeter = 25.5 cm

Let the sides be,

a = 12x cm

b = 14x cm

c = 25x cm

We know that,

Perimeter of a triangle = a + b + c

⇒ 25.5 cm = 12x cm + 14x cm + 25x cm

⇒ 25.5 cm = 51x cm

⇒ x = 0. 5

Therefore,

a = 12x cm = 12 × 0.5 cm = 6 cm

b = 14x cm = 14 × 0.5 cm = 7 cm

c = 25x cm = 25 × 0.5 cm = 12.5 cm

Clearly largest side is c = 12.5 cm