ShmoopTube

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

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Yeah, they’re a bit of a freak show.

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Find the value of y.

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Here are the potential answers...

00:16

Find the value of y… okay, easy enough.

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Well, we’ve got two triangles… we have only one piece of information for one of them…

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…and TWO pieces of information for the other.

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Makes sense to start with the triangle we know more about…

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All right, so we have a right triangle… with one side length of 6 and another of 8…

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Ah, boom. We know this guy. It’s one of those 3-4-5 dealios.

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Okay, so if the ratio is 3 to 6, and 4 to 8…

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…then our hypotenuse is also going to be double the 5… or 10.

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All right, now we have two pieces of information for the TOP triangle…

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And NOW we can bring Pythagoras into it.

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We get a squared plus b squared equals c squared. Remember that?

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4 squared plus 10 squared equals y squared.

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4 squared is 16… 10 squared is 100…

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…and 16 plus 100 is 116.

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So 116 = y squared… which makes y the square root of 116.

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116 is 4 times 29… so we can break it down into 2 times the square root of 29,

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final answer which is Choice B and we're done!

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