ShmoopTube

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

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Without them, every other necktie would have a fish on it.

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What is the length of the diagonals of a rectangle with sides equal to x and 2x?

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Here are the potential answers...

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Hm…when might we see a rectangle with diagonals in real life…?

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Perhaps we’re looking at a Confederate flag...

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…or that quilt your grandmother stitched for you…

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…or a dead Sasquatch floating in our swimming pool…

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Yeah, let’s go with the Sasquatch. We can’t bear to look at that quilt again.

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Okay, so if your pool has a width of x and a length of 2x…

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…we want to know the length of the Sasquatch,

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from the end of one hand to the tip of his opposite enormous foot.

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What we should immediately recognize is that the diagonal of any rectangle divides the

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shape into two equally sized triangles.

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So as long as we know how to determine the hypotenuse of

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a right triangle given the length of its legs…this should be a cinch.

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We’re going to fall back on our a squared plus b squared equals c squared formula…

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…so x squared plus 2x squared equals c squared. So let's rewrite it...

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2x squared is 4x squared… added to our one x squared.

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That gives us 5x squared equals c squared.

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We can take the square root of both sides to get x√5 = c.

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So our answer is C.

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Such a bummer that we’re going to have to put up with that stench another three days.

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The pool guy doesn’t come until Tuesday…

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