What is the value of x?

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1 Answer
Monzur R.
May 16, 2017

#x=4#

Explanation:

We have the triangle #RST# as a #30-60-90# right triangle. We know in such triangles that if the shorter leg has length #a# then the longer leg has length #asqrt3# and hypotenuse has length #2a#.

In #RST#, the longer leg has length #2sqrt3#. From this, we can conclude that #a# is 2 and that the hypotenuse, #RT# has length #4#.

We also have the triangle #RTQ# as a #45-45-90# right triangle with #RT=RQ#. We know from these triangles that the non-hypotenuse lengths are the same side. Since #RT=4#, #RQ=x=4#.

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