ShmoopTube

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

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Charles Manson could teach a master class on the subject.

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What is the value of x in this figure?

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And here are the potential answers...

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Okay, so what we have here is a tale of two right triangles.

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Let’s start with the bigger of the two.

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The hypotenuse is 11…one leg is the dotted vertical line, or the height,

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and the other leg is 6 plus x… whatever “x” is.

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The smaller triangle has a hypotenuse of 7, the same height, and plain ol’ x as its base.

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So, of course, because we’re dealing with triangles, we can use the

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Pythagorean Theorem to solve for the missing leg, x

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For the bigger triangle, (x + 6) squared + h squared = 11 squared.

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For the smaller one, x squared + h squared = 7 squared.

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We can simplify the second one a bit....

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So now we have x squared + h squared = 49.

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By subtracting x squared from both sides, we now have h squared = 49 - x squared…

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…and we can now take the second part – the 49 minus x squared…

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…and use it to replace the h squared in our first equation…

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…giving us x squared + 12x + 36 + (49 - x squared) = 121.

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We can add together our 36 and 49, like this…

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…and our two x squareds cancel out…

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…giving us 12x + 85 = 121.

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We’ll knock 85 off both sides to get 12x = 36…

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…and finally divide both sides by 12 to get x = 3.

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Choice B.

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