Video: Calculating the Perimeter of Figures Formed by Squares and Rectangles by Writing an Algebraic Expression

Express the perimeter of the figure below in terms of π‘₯.

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Video Transcript

Express the perimeter of the figure below in terms of π‘₯.

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 16π‘₯, 16π‘₯, π‘₯, and 15π‘₯. So in order to find the perimeter, we need to find the remaining side length. 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 16π‘₯ plus π‘₯. And combining like terms, we get 17π‘₯. So we can label the missing side 17π‘₯. Now this last missing piece create an entire side with the 15π‘₯. So this side will be represented by 15π‘₯ plus question mark. So we’re excluding this yellow piece. It is just the pieces that are parallel the question mark and the 15π‘₯.

So that 15π‘₯ plus question mark will be the same length as the 16π‘₯. So we can set it equal to 16π‘₯. So 15π‘₯ plus question mark equals 16π‘₯. So let’s subtract 15π‘₯ from both sides. So question mark is equal to π‘₯ or one π‘₯. So this length is π‘₯.

So now we have every single side length. So now, we can find the perimeter by adding them all together. So we have 16π‘₯ plus 16π‘₯ plus π‘₯ plus π‘₯ plus 15π‘₯ plus 17π‘₯. And adding these all together will give us the perimeter. And we get 66π‘₯. Therefore, our final answer in terms of π‘₯ will be 66π‘₯ length units.

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