Question

The perimeter of the triangle is 13 inches. What is the length of the shortest side?

Answer 1

3 in

Explanation:

Sum of all sides of ∆ = perimeter

Given that it has a perimeter of 13 in, and the following sides: (x - 5) in, x/2 in, and 6 in, therefore:

`x - 5 + (x)/(2) + 6 = 13`

Solve to find the value of x

`(2x - 10 + x + 12)/(2) = 13`

`(3x + 2)/(2) = 13`

Multiply both sides by 2

`(3x + 2)/(2)*2 = 13*2`

`3x + 2 = 26`

Subtract 2 from both sides

`3x + 2 - 2 = 26 - 2`

`3x = 24`

Divide both sides by 3

`(3x)/(3) = (24)/(3)`

`x = 8`

The shortest side = (x - 5) in

Plug in the value of x

= (8 - 5) in

= 3 in