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

The shortest side of the triangle is 3 inches.

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
`(1)/(6)x`

And the second side be
`(1)/(3)x`.

And the third side be
`(1)/(4)x`.

According to question:

`(1)/(6)x+(1)/(3)x+(1)/(4)x=13.5`

⇒
`(x)/(6)+(x)/(3)+(x)/(4)=13.5`

Adding all the variables by taking common denominator we get:

⇒
`(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.