Answer:
The shortest side of the triangle is 3 inches.
Step-by-step explanation:
Given:
The ratio of the measure of the sides of the triangle is 1/6: 1/3: 1/4.
The perimeter = 13.5 inches.
Now, to find the shortest side.
Let the one side be [tex]\frac{1}{6}x[/tex]
And the second side be [tex]\frac{1}{3}x[/tex].
And the third side be [tex]\frac{1}{4}x[/tex].
According to question:
[tex]\frac{1}{6}x+\frac{1}{3}x+\frac{1}{4}x=13.5[/tex]
⇒[tex]\frac{x}{6}+\frac{x}{3}+\frac{x}{4}=13.5[/tex]
Adding all the variables by taking common denominator we get:
⇒[tex]\frac{9x}{12}=13.5[/tex]
Multiplying both sides by 12 we get:
⇒[tex]9x=162[/tex]
Dividing both sides by 9 we get:
⇒[tex]x=18[/tex]
Thus, the sides of the triangle are:
1/6×18=3 inches.
1/3×18=6 inches.
1/4×18=9/2=4.5 inches.
Therefore, the shortest side of the triangle is 3 inches.
