Given:
The ratio of the measures of the three sides of a triangle is [tex]\dfrac{1}{4}:\dfrac{1}{3}:\dfrac{1}{6}[/tex].
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 [tex]\dfrac{1}{4}x,\dfrac{1}{3}x,\dfrac{1}{6}x[/tex] respectively (in cm).
Its perimeter is 31.4 centimeters.
[tex]\dfrac{1}{4}x+\dfrac{1}{3}x+\dfrac{1}{6}x=31.4[/tex]
[tex]\dfrac{3x+4x+2x}{12}=31.4[/tex]
[tex]\dfrac{9x}{12}=31.4[/tex]
[tex]\dfrac{3x}{4}=31.4[/tex]
On further simplification, we get
[tex]3x=4\times 31.4[/tex]
[tex]3x=125.6[/tex]
Divide both sides by 3.
[tex]x=\dfrac{125.6}{3}[/tex]
[tex]x=41.867[/tex]
Now, the sides of triangle are
[tex]\dfrac{1}{4}(41.867)=10.467[/tex]
[tex]\dfrac{1}{3}(41.867)=13.956[/tex]
[tex]\dfrac{1}{6}(41.867)=6.978[/tex]
Therefore, the length of the shortest side is 6.978 cm.
