SOLUTION: the hypotenuse of a right triangle is twice as long as one of the legs and 6 inches longer than the other. what are the lengths of the sides of the triangle

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Question 212133: the hypotenuse of a right triangle is twice as long as one of the legs and 6 inches longer than the other. what are the lengths of the sides of the triangle
Answer by Mr. Kong(2) (Show Source):
You can put this solution on YOUR website!
This triangle is a 30-60-90 triangle because one of the legs doubled is the hypotenuse.
Remember similar triangles have equal proportions.
Let x be the hypotenuse, y the leg half of x, and z the other leg.
sqrt(3)/2=z/x
x=z+6 so
sqrt(3)/2 = z/(z+6)
Solve the proportion by cross multiplying to find z.
z is (sqrt(3)*6)/(2-sqrt(3)). Approximation z = 38.8
x is approximately 44.8 since you add 6 to z.
y is half of x so y = 22.4

Test these numbers with the Pythagorean theorem.