Question

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

Answer 1

Answer:

3 in

Step-by-step 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:

$x - 5 + \frac{x}{2} + 6 = 13$

Solve to find the value of x

$\frac{2x - 10 + x + 12}{2} = 13$

$\frac{3x + 2}{2} = 13$

Multiply both sides by 2

$\frac{3x + 2}{2}*2 = 13*2$

$3x + 2 = 26$

Subtract 2 from both sides

$3x + 2 - 2 = 26 - 2$

$3x = 24$

Divide both sides by 3

$\frac{3x}{3} = \frac{24}{3}$

$x = 8$

The shortest side = (x - 5) in

Plug in the value of x

= (8 - 5) in

= 3 in