Suppose a right triangle has one leg of the length 5cm. the hypotenuse is twice as long as the other leg. find the missing two sides of the right triangle

According to the Pythagorean Theorem, x^2 + y^2 = hyp^2.

Let x = 5cm be one leg.

If the hyp is twice as long as the other leg, then hyp = 2y.  

Then x^2 + y^2 = hyp^2 becomes

       (5 cm)^2 + y^2 = (2y)^2.  We need to solve this for y.
                          
                                                                                         25 cm^2
25 cm^2 + y^2 = 4y^2, or 25 cm^2 = 3y^2.  Then y^2 =
                                                                                               3

and y = + sqrt( [25 cm^2] / 3 ), or   y = + 5 / sqrt(3), or y = 5sqrt(3) / 3.

The "other side" thus has length   y = 5sqrt(3) / 3  

and the hyp has length 2y = 2 [ 5sqrt(3) / 3 ]  =  10 sqrt(3) / 3 

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