SOLUTION: A right angled triangle with hypotenuse 20cm. A square 6cm placed in the right angle of the triangle. The hypothenuse touches the top right corner of the square. What is length o

Question 1074446: A right angled triangle with hypotenuse 20cm. A square 6cm placed in the right angle of the triangle. The hypothenuse touches the top right corner of the square.
What is length of other two sides?
I started usi g similar triangles and called base (x+6) and height (y+6) getting
y=36/x. Then use Pythagoras. But can't simplify the complicated algebra I get after that.
Can anyone help?
Found 2 solutions by Alan3354, Fombitz:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
I did the same, got
x^4 + 12x^3 - 328x^2 + 432x + 1296 = 0
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I used a graph to find x.
x =~ 3.0405155
--> the x side is 6 plus that, or that can be the y side, they're interchangeable.
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I'm looking for another method, don't have one yet.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
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By Pythagoras,

By similar triangles,

So,

Substituting,

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Graphing finds two positive solutions,
and
with corresponding x values,

and
So then the lengths of the other sides are,

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