The longest side of a triangle is six more units that the shortest side. The third side is twice the length of the shortest side. If the perimeter of the triangle is 25 units, write and solve an equation to find the length of all three sides of the triangle.

Let s = shortest side, then longest = s+6 and 2s = third side.

s + (s+6) + 2s = 25

Solve for s then the others.

To solve this problem, we'll use variables to represent the lengths of the sides of the triangle.

Let's say the shortest side has a length of x units.
According to the problem, the longest side is 6 units more than the shortest side, so its length would be (x + 6) units.
The third side is twice the length of the shortest side, so it would be (2x) units long.

The perimeter of a triangle is the sum of the lengths of its three sides. In this case, the perimeter is given as 25 units. So we can write the equation:

x + (x + 6) + (2x) = 25

Now let's solve this equation to find the value of x:

x + x + 6 + 2x = 25
4x + 6 = 25
4x = 25 - 6
4x = 19
x = 19/4
x = 4.75

Now we can substitute the value of x back into the expressions for the lengths of the sides to find their values:

Shortest side = x = 4.75 units
Longest side = x + 6 = 4.75 + 6 = 10.75 units
Third side = 2x = 2 * 4.75 = 9.5 units

So, the lengths of the sides of the triangle are 4.75 units, 10.75 units, and 9.5 units.