Question

What’s the value of X, Y, and Z

Answer 1

• x = y = 6√6
• z = 6√3

Explanation:

For problems like these, it is helpful to remember the ratios of the side lengths in these special triangles.

45°-45°-90° triangle: 1 : 1 : √2

30°-60°-90° triangle: 1 : √3 : 2

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This means ...

z : 18 : horizontal line = 1 : √3 : 2

z = 18/√3 = 6√3

horizontal line = 2(6√3) = 12√3

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And ...

x : y : horizontal line = 1 : 1 : √2

x = y = (horizontal line)/√2 = (12√3)/√2 = 6√6

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Additional comment

The lengths are easily found as values with a square root in the denominator. Generally, we want the denominator to be a rational number, so we make use of the fact ...

1/√n = (√n)/n