Express the perimeter of the figure below in terms of 𝑥.
So what is a perimeter? A perimeter is a distance around a shape. So let’s go ahead and highlight some of the lengths that we are ready know. Here we have 16𝑥, 16𝑥, 𝑥, and 15𝑥. So in order to find the perimeter, we need to find the remaining side lengths. Let’s begin with this one.
It is the exact same length as these two yellow lengths, put together. So this entire side will be 16𝑥 plus 𝑥. And combining like terms, we get 17𝑥. So we can label the missing side 17𝑥. Now this last missing piece create an entire side with the 15𝑥. So this side will be represented by 15𝑥 plus question mark. So we’re excluding this yellow piece. It is just the pieces that are parallel the question mark and the 15𝑥.
So that 15𝑥 plus question mark will be the same length as the 16𝑥. So we can set it equal to 16𝑥. So 15𝑥 plus question mark equals 16𝑥. So let’s subtract 15𝑥 from both sides. So question mark is equal to 𝑥 or one 𝑥. So this length is 𝑥.
So now we have every single side length. So now, we can find the perimeter by adding them all together. So we have 16𝑥 plus 16𝑥 plus 𝑥 plus 𝑥 plus 15𝑥 plus 17𝑥. And adding these all together will give us the perimeter. And we get 66𝑥. Therefore, our final answer in terms of 𝑥 will be 66𝑥 length units.