Finding missing side length when given perimeter | Math | 3rd grade | Khan Academy

The perimeter of the figure is 24 centimeters. What is the length of the missing side?

So, we're told this figure down here has a perimeter of 24 centimeters. The perimeter is 24 centimeters, so what that tells us is that the distance around the entire outside is 24 centimeters.

But what we want to know is what is the length of the missing side? Well, the missing side is going to be the side we're not told, so it will be this one here because we have this question mark. It's missing; it is not labeled.

So, we've got to figure out what number should go on this missing side so that the entire length is 24 centimeters. Let’s start with what we do know. We know that this top length, this top side, has a length of six centimeters. Plus, going down the left has a length of five more centimeters. Plus, across the bottom is four more centimeters and the last known side is another four centimeters.

So, when we add all those plus this mystery side, we should get a perimeter of 24. The entire distance, all of this, the 6 plus the 5 plus the 4 plus the 4 plus this mystery number should get us to a perimeter of 24.

So, let's add over here and try to make it a little simpler to find our missing side. I can add in any order and I love making tens. So I'm going to say 6 and 4 is 10, 10 plus 5 is 15, and 15 plus 4 more is 19.

So we know where 19 centimeters come from on this shape. Here's the 19 centimeters, outlined in blue. So, how many more centimeters, what length must this missing side be to get us a total distance around the outside of 24 centimeters? We can do that math.

19 plus 1 more is 20, and then plus 4 more to 24. So, one more to 20 and four more; that's a total of five more. So, the missing side length is 5 centimeters. This side right here must be 5 centimeters in order for the total perimeter to be 24.

Okay, let's look at one more. This time it says that the perimeter of a rectangle is 32 meters and one side is 11 meters. What is the length of the missing side?

So again, we have a missing side. So let's visualize this. Let's draw ourselves a rectangle here. This is what a rectangle looks like, and we know that one side is 11 centimeters, so one side is 11 or meters, excuse me.

And because we know that this side is 11 meters, we also know that this side is 11 meters. On a rectangle, opposite sides are equal, so those two we know. But what we don't know are this top and the bottom; those are the missing sides.

So, what are those side lengths? Well, again, we know we have a perimeter of 32 meters. We're told right here, the perimeter is 32 meters. So the question is, 11 plus 11 for these two sides, 11 and plus some mystery number, and then plus that same mystery number because these two sides are equal, and that has to give us a total, a total of equals 32 because 32 is the total distance around the outside.

So let's add the 11's. 11 plus 11 is 22, so 22 plus how many more gets us to 32? Well, 22 plus 10 more is 32, but if we label one of these sides as 10, then the other one would have to be zero, so they have to be equal.

So, how can we equally split those 10 meters between the two sides? Half of 10 is 5. So these sides are each 5 meters. 22, 5 plus 5 is 10, 22 plus 10 is 32. So, the missing side length is 5 meters.