Final answer:
To find the length of the third side of the triangle, you can set up an equation using the formula for the perimeter of a triangle. Simplify the equation and solve for the variable. Substitute the value of the variable back into the equation to find the length of the third side.
Step-by-step explanation:
To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. In this case, the perimeter is given as 23x-7. So, we can set up the equation: (5x+7) + (8x-9) + third side = 23x-7.
Next, we combine like terms and solve for the third side: 13x + third side - 2 = 23x - 7. Simplifying further, we get 13x - 21 = 23x - 7. Moving the variable terms to one side and the constants to the other side, we have 21 - 7 = 23x - 13x.
Continuing to solve, we get 14 = 10x. Dividing both sides by 10, we find x = 1.4. Finally, substitute this value of x into the equation to find the length of the third side: third side = 23(1.4) - 7 = 32.2 - 7 = 25.2.