Question

5. Find the perimeter for the figure. Show the set-up and allwork.

Answer 1

Step-by-step 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:

`7,9x,10,3x,12,4x,15,2x`

Then their sum is:

`7+9x+10+3x+12+4x+15+2x`

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:

`(7+10+12+15)+(9x+3x+4x+2x)`

We can use the distributive property in the terms with x. For example:

`ax+bx+cx=(a+b+c)x`

We use this and we also add the constants so we get:

`\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}`Answer

Then the answer is that the perimeter of the figure is 18x+44.