Explanation
The perimeter of a polygon is given by the sum of the length of its sides. For the polygon in the picture we have the following side lengths:
[tex]7,9x,10,3x,12,4x,15,2x[/tex]
Then their sum is:
[tex]7+9x+10+3x+12+4x+15+2x[/tex]
We can group like terms. Like terms are terms multiplied by the same power of x. In this case we have two groups of like terms: constants and terms multiplied by x. Then we group them:
[tex](7+10+12+15)+(9x+3x+4x+2x)[/tex]
We can use the distributive property in the terms with x. For example:
[tex]ax+bx+cx=(a+b+c)x[/tex]
We use this and we also add the constants so we get:
[tex]\begin{gathered} (7+10+12+15)+(9x+3x+4x+2x)=44+(9+3+4+2)x \\ 44+(9+3+4+2)x=44+18x \end{gathered}[/tex]Answer
Then the answer is that the perimeter of the figure is 18x+44.
