Answer:
x = (20/3)√3 cm ≈ 11.547 cm
Step-by-step explanation:
You know from the Pythagorean theorem that the square of the hypotenuse of a right triangle is the sum of the squares of the other two sides. Applying that fact twice gives ...
AC² = AB² +BC²
FA² = FC² +AC²
Substituting for AC² using the first equation gives ...
FA² = FC² +AB² +BC²
Using the given value for side lengths, this is ...
FC² = x² +x² +x² = 3x²
FC = x√3 . . . . take the square root
20 cm = x√3 . . . . substitute given value for FC
x = 20 cm/√3 . . . divide by the coefficient of x
x = (20/3)√3 cm ≈ 11.547 cm . . . . with denominator rationalized
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Additional comment
The reciprocal of √n can be written with a rational denominator as (√n)/n. This value can be obtained by rewriting 1/√n as √(n/n²).
