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.
<em>Let the one side be
</em>
<em>And the second side be
.</em>
<em>And the third side be
.</em>
According to question:

⇒
Adding all the variables by taking common denominator we get:
⇒
<em>Multiplying both sides by 12 we get</em>:
⇒
<em>Dividing both sides by 9 we get</em>:
⇒
Thus, <em>the sides of the triangle are</em>:
<u>1/6×18=3 inches.</u>
<u>1/3×18=6 inches.</u>
<u>1/4×18=9/2=4.5 inches</u>.
Therefore, the shortest side of the triangle is 3 inches.