one side of a triangle is 3 inches shorter than twice the length of the shorest side. the third side is 5 inches longer than the shorest side. if the perimeter is 110 inches, find the lengths of all three sides

Let x = shortest side.

x + 2x - 3 + x + 5 = 110

4x + 2 = 110
4x = 108
x = 27

To find the lengths of the sides of the triangle, let's assign variables. Let's call the shortest side x inches.

According to the given information:
- One side of the triangle is 3 inches shorter than twice the length of the shortest side. This can be expressed as 2x - 3 inches.
- The third side is 5 inches longer than the shortest side. This can be expressed as x + 5 inches.

The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is 110 inches:

Perimeter = Shortest side + Side length (2x - 3) + Side length (x + 5)

Now, we can write the equation and solve for x:

110 = x + (2x - 3) + (x + 5)

Simplifying the equation:
110 = 4x + 2

Subtracting 2 from both sides:
108 = 4x

Dividing both sides by 4:
x = 27

Now, we know that the shortest side is 27 inches. We can plug this value back into the expressions we found earlier to calculate the lengths of the other two sides.

One side of the triangle = 2x - 3
= 2(27) - 3
= 54 - 3
= 51 inches

The third side of the triangle = x + 5
= 27 + 5
= 32 inches

Therefore, the lengths of the sides of the triangle are:
Shortest side: 27 inches
One side: 51 inches
Third side: 32 inches