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:
[tex] x - 5 + \frac{x}{2} + 6 = 13 [/tex]
Solve to find the value of x
[tex] \frac{2x - 10 + x + 12}{2} = 13 [/tex]
[tex] \frac{3x + 2}{2} = 13 [/tex]
Multiply both sides by 2
[tex] \frac{3x + 2}{2}*2 = 13*2 [/tex]
[tex] 3x + 2 = 26 [/tex]
Subtract 2 from both sides
[tex] 3x + 2 - 2 = 26 - 2 [/tex]
[tex] 3x = 24 [/tex]
Divide both sides by 3
[tex] \frac{3x}{3} = \frac{24}{3} [/tex]
[tex] x = 8 [/tex]
The shortest side = (x - 5) in
Plug in the value of x
= (8 - 5) in
= 3 in
