Question

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

Answer 1

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.