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ACT Math 4.2 Plane Geometry 251 Views


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ACT Math: Plane Geometry Drill 4, Problem 2. If x, y, and z are all integer values, which of the following cannot be the ratio of x:y:z?

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English Language

Transcript

00:02

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

00:06

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

00:10

of x:y:z?

00:12

And here are your options...

00:16

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

00:20

aren't fractions or decimals. We also know that

00:23

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

00:29

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

00:35

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

00:40

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

00:43

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

00:46

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

00:50

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

00:57

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

01:04

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

01:16

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

01:30

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

01:34

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

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