SOLUTION: What is the area of a 30-60-90 triangle if the middle side is equal to 9?

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Question 885401: What is the area of a 30-60-90 triangle if the middle side is equal to 9?

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Special triangle, half of an equilateral triangle. If x is the length of the short side of the 30-60-90 triangle, then the long side is the hypotenuse of 2x. The other side is your given middle side of 9 units.

%281%2F2%29x%2A9 is area; and %282x%29%5E2=9%5E2%2Bx%5E2 using Pythagorean Theorem for the Right Triangle.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
What is the area of a 30-60-90 triangle if the middle side is equal to 9?


As the MIDDLE side represents the longer leg, area of triangle is: %281%2F2%29%289%29%289%2Fsqrt%283%29%29

highlight_green%28highlight_green%28%2827sqrt%283%29%29%2F2%29%29 units%5E2, or highlight_green%28highlight_green%2813.5sqrt%283%29%29%29 units%5E2

You can do the check!! 



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