ShmoopTube

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Here’s your shmoop du jour, brought to you by the number 10.

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Which is the biggest number we can count up to without removing our socks.

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If an equilateral triangle has side length equal to 10, what is the length of its altitude?

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Here are the potential answers...

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Alright, down to business.

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The altitude of a triangle always runs perpendicular to its base…

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…and we can indeed see that a couple of right angles are formed at the bottom.

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Which is dandy news.

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Now we have ourselves a pair of right triangles.

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We can deduce that the base of each right triangle is 5…

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…since the length of each full side of the equilateral triangle is 10…

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…and our altitude line bisects it.

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Yup…slices it right down the middle…like that poor worm you disposed of in biology.

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So…now that we have the length of two sides of our right triangle…

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…5 for the base and 10 for the hypotenuse…

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…we can apply our buddy Pythagoras and his theorem.

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5 squared plus our altitude squared equals 10 squared.

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Or… 25 plus our altitude squared equals 100.

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So the altitude is going to be the square root of the difference,100 - 25, or 75.

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Which simplifies to the square root of 25 times 3…

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…or 5 square root of 3 and the answer is C.

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Beautiful.

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