ShmoopTube

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

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If it wasn’t for the tattoo, we wouldn’t be able to tell them apart.

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Triangle ABC is similar to triangle DEF. What is the perimeter of triangle DEF?

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Okay, we’ve got a couple of similar triangles here.

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Apparently triangles of a feather flock together...

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All right, so these are both right triangles…

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…and one of them has a leg with length 6 and a hypotenuse with length 10…

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…Hello! Looks like we’ve got a 3-4-5 triangle...

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Both known distances have been doubled from the original 3-4-5 ratio…

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…so we know we have to double the missing length as well.

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Four times two is eight… and we have a triangle with sides of 6, 8 and 10.

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Plugging those numbers into our internal adding machine… we get a total perimeter of 24.

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Now, before you waste gobs of time trying to figure out what the lengths of the sides in our other triangle are…

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…just note that the one side we DO know is 2/3 of the corresponding side in triangle number one.

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These triangles are similar… so the perimeter is going to carry over the same ratio.

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We’ll take 24 times 2/3… to get 16…and that’s our answer. We're done!

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