ShmoopTube

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Sometimes, things go missing.

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It happens to the best of us…

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We went to a restaurant and took out our retainer, once, and it was lost, never to be seen again… [Girl at a restaurant losing her retainer]

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…at least, until dessert came.

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Seriously, how'd it get in there?

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The world will never know.

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Anyway, sometimes when we're doing math related to areas and perimeters, we have to deal with [Teacher discussing area and perimeters in Math class]

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missing numbers…

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…but luckily there are tried and true ways of finding them.

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So let's take a look at this rectangle.

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To find its area, all we need to do is multiply its length by its width…[Area calculation beside a rectangle]

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…so we'd multiply eight inches…

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…by four inches…

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…to find 32 square inches.

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No sweat.

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But what about this one?

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Here we know the length of one side, and the area, but not the length of the other side. [Rectangle displaying the area and the length of one side but not the other side]

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Is there any way to find the length of that missing side?

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Do we need to put up missing posters on every lamppost in town? [Missing sign poster of a rectangles missing side length]

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Nope!

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Luckily for us – and for the posts – we just need to do some math.

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Let's think back to the formula for the area of a rectangle: the area of a rectangle is [Rectangle with an area of 15 square inches]

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equal to its length times its width.

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We know that its area is fifteen square inches…

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…and its length is five inches, so the width has to be a number that, when multiplied by

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five, gives us fifteen.

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If we remember anything from our multiplication tables, we know there's only one number that [Multiplication tables on a piece of paper]

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does that: three.

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So the rectangle has a width of three inches.

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And we didn't need to put up a single missing poster.

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Thanks, math, for saving us all that tape! [Man sticking missing poster on lamp posts]

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We can use a similar process with perimeters.

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Take a look at this rectangle.

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We know that two sides are each six inches long, and that it has a total perimeter of

01:42

20 inches, but what are the lengths of the remaining sides? [Rectangle with missing lengths]

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Let's take a look at our formula for perimeter.

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It's what we get when we add up the lengths of all the sides. [Formula for perimeter beside a rectangle]

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We know that the perimeter is twenty inches…

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…and two of the sides are six inches long.

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Plus, since the other two sides are opposite sides of a rectangle, they're the same length.

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But what is that length? [Question mark inside a rectangle]

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We could try five inches.

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Unfortunately, when we add those lengths up, we get 22 inches, not 20.

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And unless there are some big changes in Mathland, 22 is definitely not equal to 20.

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Let's try something slightly smaller, like four inches.

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And…..bingo!

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We're in luck!

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This math actually works out, so the remaining sides are each four inches long. [Rectangle displaying the number 4 for the missing lengths]

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Now…could someone help us find our retainer?

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We're thinking it might be in the crème brulee….[Retainer lodged in the middle of a creme brulee]

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