Question Video: Calculating the Side Length of a Square given Its Perimeter Mathematics

What is the side length of a square whose perimeter is 12 cm?


Video Transcript

What is the side length of a square whose perimeter is 12 centimeters?

Let’s start by recalling how a square is defined. We can say that a square is a parallelogram with four congruent angles and four congruent sides. So, for example, we could draw a square like this. Each side length will be the same, and each angle measure will be 90 degrees, since the sum of the angle measures in any quadrilateral is 360 degrees. The fact a square is also a parallelogram means that both pairs of opposite sides are parallel.

Now, we need to consider what the side length of a square would be given that its perimeter is 12 centimeters. We could define the side length to be π‘₯ centimeters. And as the side lengths are all congruent, then every side length would be π‘₯ centimeters. Given that the perimeter is the distance around the outside edge of a polygon, then we could say that the square has a perimeter of π‘₯ plus π‘₯ plus π‘₯ plus π‘₯, or four π‘₯ centimeters.

Combined with the fact that the perimeter of this particular square is 12 centimeters, we can write that 12 is equal to four π‘₯. Then, dividing both sides of the equation by four, we have that π‘₯ is equal to three centimeters. And so we can give the answer that a square with a perimeter of 12 centimeters must have a side length of three centimeters.

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