The lengths of the sides of a triangle are 2x+5, x-3, and 3x+1. The perimeter of the triangle is 45 in. What are the lengths of the sides?

2x + 5 + x - 3 + 3x + 1 = 45

6 x + 3 = 45
6x = 42
x = 7
so
2x+ 5 = 19 etc etc

To find the lengths of the sides of the triangle, we can use the fact that the perimeter of a triangle is equal to the sum of the lengths of its sides.

According to the problem, the lengths of the sides of the triangle are given as 2x + 5, x - 3, and 3x + 1.

So, we can set up an equation using the given information:

(2x + 5) + (x - 3) + (3x + 1) = 45

Now, let's simplify the equation:

2x + x + 3x + 5 - 3 + 1 = 45

Combining like terms:

6x + 3 = 45

Next, let's isolate the variable:

6x = 45 - 3

6x = 42

Divide both sides of the equation by 6:

x = 42/6

x = 7

Now that we have found the value of x, we can substitute it back into the expressions for the lengths of the sides to find their values.

Sides of the triangle:
Side 1: 2x + 5 = 2(7) + 5 = 14 + 5 = 19
Side 2: x - 3 = 7 - 3 = 4
Side 3: 3x + 1 = 3(7) + 1 = 21 + 1 = 22

Therefore, the lengths of the sides of the triangle are 19, 4, and 22.