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 $\dfrac{1}{4}:\dfrac{1}{3}:\dfrac{1}{6}$.

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 $\dfrac{1}{4}x,\dfrac{1}{3}x,\dfrac{1}{6}x$ respectively (in cm).

Its perimeter is 31.4 centimeters.

$\dfrac{1}{4}x+\dfrac{1}{3}x+\dfrac{1}{6}x=31.4$

$\dfrac{3x+4x+2x}{12}=31.4$

$\dfrac{9x}{12}=31.4$

$\dfrac{3x}{4}=31.4$

On further simplification, we get

$3x=4\times 31.4$

$3x=125.6$

Divide both sides by 3.

$x=\dfrac{125.6}{3}$

$x=41.867$

Now, the sides of triangle are

$\dfrac{1}{4}(41.867)=10.467$

$\dfrac{1}{3}(41.867)=13.956$

$\dfrac{1}{6}(41.867)=6.978$

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