Question

The ratio of the measure of the sides of the triangle is 1/6: 1/3: 1/4 if the perimeter of the triangle is 13.5 inches find the shortest side

Answer 1

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 $\frac{1}{6}x$

And the second side be  $\frac{1}{3}x$.

And the third side be  $\frac{1}{4}x$.

According to question:

$\frac{1}{6}x+\frac{1}{3}x+\frac{1}{4}x=13.5$

⇒$\frac{x}{6}+\frac{x}{3}+\frac{x}{4}=13.5$

Adding all the variables by taking common denominator we get:

⇒$\frac{9x}{12}=13.5$

Multiplying both sides by 12 we get:

⇒$9x=162$

Dividing both sides by 9 we get:

⇒$x=18$

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.