Question

The side of a triangle are in the ratio 1/3: 1/4: 1/5 and its perimeter is 94 cm. The length of the smallest side is

Answer 1

Answer:

Step-by-step explanation:

Ratio of sides=(1/3:1/4:1/5)×60(L.C.M) =20:15:12

Perimeter=20+15+12=47unit

Given perimeter =94cm

47unit=94

1unit=2cm

Asking for the length of smallest side , smallest side is 12×2=24

The smallest side is 24cm.

Answer 2

Given:

The sides of a triangle are in the ratio 1/3: 1/4: 1/5 and its perimeter is 94 cm.

To find:

The length of the smallest side.

Solution:

As we know that the perimeter of a triangle is equal to the sum of all its three sides.

Now, as given

The sides of a triangle are in the ratio 1/3: 1/4:1/5. So, let the highest common factor between all three sides of the triangle be x.

So,

the three sides of the triangle are

$\frac{1}{3} x \: \: \: \: (i)$

$\frac{1}{4} x \: \: \: (ii)$

$\frac{1}{5} x \: \: \: (iii)$

as 1/5 has the largest denominator, so it is the smallest side of the triangle.

Now,

the perimeter of the triangle = 94cm

So,

$\frac{1}{3} x + \: \frac{1}{4} x \: + \: \frac{1}{5} x = 94$

On taking 60 as LCM, we have,

$\frac{20x + 15x + 12x}{60} = 94$

$\frac{47x}{60} = 94$

$x = \frac{94 \times 60}{47}$

$x = 2 \times 60$

$x = 120$

On putting the value of x in the (iii), we get

$\frac{1}{5} \times 120$

$= 24 \: cm$

Hence, the length of the smallest side is 24cm.