ShmoopTube

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Here’s your shmoop du jour, brought to you by hypotenuse.

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It's always right between the legs.

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This cube has side lengths of 4.

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Point B is in the center of the top side and Point A is in the center of the right side.

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Find the length of AB.

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Here are the potential answers...

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This problem is actually a lot simpler than it appears, and

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really just involves knowing one simple rule about triangles...

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What we do know is that the side length of each side is 4…

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…and that these points are located exactly halfway across a couple of the sides.

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Well, using advanced calculus we can determine that half of 4 is 2…

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…so B has to be 2 away from each edge, and A has to be the same.

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So if we go ahead and draw that imaginary line from B to A…

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…we create an isosceles triangle, with each leg measuring “2.”

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Now all we have to do is apply our knowledge of isosceles triangles…

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…specifically, that the legs and hypotenuse always have a ratio of x to x to x square root of 2.

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And since we have our x value – “2”…

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…our hypotenuse, or line AB, must be 2 square root of 2.

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Answer B.

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