ShmoopTube

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Time for your daily dose of shmoop. This won't hurt a bit.

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If x, y, and z are all integer values, which of the following cannot be the ratio

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of x:y:z?

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And here are your options...

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All we know about this triangle is that its angles are integer values, meaning that they

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aren't fractions or decimals. We also know that

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the sum of a triangle's angles always equal 180 degrees. So... since the ratios of the

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angles are always relative to 180 degrees, we have to look for the ratio that can't

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allow the angles to be integers. In English, that basically means that, since

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we're dividing up 180 degrees into little parts...

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...180 has to be divisible by the total number

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of parts in the ratio. The question is asking for the ratio that

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can't be possible, so we have to look for the one that isn't divisible by 180. Let's

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try: A: 1 + 2 + 3 = 6 and 180 / 6 = 30

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B: 1 + 2 + 2 = 5, 180 / 5 = 36 C: 1 + 1 + 2 = 4, 180 / 4 = 45

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D: 1 + 2 + 4 = 7, 180 / 7 = 25.715 E: 1 + 2 + 6 = 9, 180 / 9 = 20

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Our answer is D because it doesn't produce an integer value, which means that each part

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is not an integer, which ultimately means that the angles can't be integers either.

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