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What is the value of x?

What is the value of x?-example-1

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Triangle QRT has a given 45-deg angle and a right angle.
The third angle is also 45 deg, so it is a 45-45-90 triangle and sides RT and RQ are congruent.

Triangle RST is a 30-60-90 triangle. Side RT is twice the length of side ST.
Side RS is sqrt(3) times the length of side ST.

ST = (2sqrt(3))/sqrt(3) = 2

RT = 2ST = 3 * 2 = 4

x = RQ = RT = 4

x = 4
User ZheFrench
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