Question

The ratio of the measures of the three sides of a triangle is 1/4:1/3:1/6 and its perimeter is 31.4 centimetres find the length of the shortest side

Answer 1

Given:

The ratio of the measures of the three sides of a triangle is
`(1)/(4):(1)/(3):(1)/(6)`.

Its perimeter is 31.4 centimeters

To find:

The shortest side of the triangle.

Solution:

Let the measures of the three sides of a triangle are
`(1)/(4)x,(1)/(3)x,(1)/(6)x` respectively (in cm).

Its perimeter is 31.4 centimeters.

`(1)/(4)x+(1)/(3)x+(1)/(6)x=31.4`

`(3x+4x+2x)/(12)=31.4`

`(9x)/(12)=31.4`

`(3x)/(4)=31.4`

On further simplification, we get

`3x=4* 31.4`

`3x=125.6`

Divide both sides by 3.

`x=(125.6)/(3)`

`x=41.867`

Now, the sides of triangle are

`(1)/(4)(41.867)=10.467`

`(1)/(3)(41.867)=13.956`

`(1)/(6)(41.867)=6.978`

Therefore, the length of the shortest side is 6.978 cm.