The perimeter of a scalene triangle is 14.5 cm. the longest side is twice that of the shortest side. which equation can be used to find the side lengths if trhe longest side measures 6.2 cm?

S = length of small side
M = length of medium side
L = length of long side

The triangle is scalene meaning that the three sides (S, M, L) are all different. If any two sides were equal, then we'd have an isosceles triangle. If all sides were the same, then the triangle would be equilateral. 

"The longest side is twice that of the shortest side" tells us that L = 2*S
The longest side is given to be 6.2 cm, so L = 6.2 and we can find S to be...

L = 2*S
6.2 = 2*S
2*S = 6.2
S = 6.2/2
S = 3.1

The longest side is 6.2 leads to the shortest side being 3.1

Add up the three sides and set that sum equal to the perimeter 14.5

(short side) + (medium side) + (long side) = perimeter
S + M + L = 14.5
3.1 + M + 6.2 = 14.5
M + 9.3 = 14.5

It's not clear where your teacher wants you to stop, so this might be a good place. If you wanted, you can isolate M by subtracting 9.3 from both sides