The perimeter of the polygon below is 9x-1. Find the expression for the missing side length.
There are 5 expressions: 3x-4, x-5, x+1, 2x+3, and ?. I got ?=2x-6. I added all the equation and minus it from 9x-1.
2x+4
To find the expression for the missing side length of the polygon, we need to subtract the sum of the given side lengths from the total perimeter of the polygon.
Given side lengths: 3x-4, x-5, x+1, and 2x+3.
The sum of the given side lengths is: (3x-4) + (x-5) + (x+1) + (2x+3).
To find the missing side length, we subtract the sum of the given side lengths from the total perimeter of the polygon, which is 9x-1.
The missing side length is therefore:
(9x-1) - [(3x-4) + (x-5) + (x+1) + (2x+3)].
Now we can simplify this expression:
(9x-1) - [3x-4 + x-5 + x+1 + 2x+3] (Remove parentheses)
9x-1 - (3x-4 - x+5 - x-1 - 2x-3) (Distribute the negative sign)
9x-1 - (3x-4-x+5-x-1-2x-3)
9x-1 - 3x+4-x-5+x+1+2x+3
9x - 3x - x + x - 2x - 1 + 4 + 5 + 1 + 2x + 3
(9x - 3x - x - x + x + 2x) + (-1 + 4 + 5 + 1 + 3)
6x + 12
Therefore, the expression for the missing side length is 6x + 12.