A geometry problem by A Former Brilliant Member

If this altitude splits the hypotenuse into segments of lengths $x$ and $10-x$ , then by the Property of Geometric Means in a right triangle we get:

$\frac{6}{x} = \frac{10-x}{6} \Rightarrow x^2 - 10x + 36 = 0 \Rightarrow x = \frac{10 \pm \sqrt{10^2 - 4(1)(36)}}{2} = \frac{10 \pm \sqrt{-44}}{2} = 5 \pm \sqrt{11}i$

which implies an impossible scenario!

circumscribe the triangle in the circle. you will see that the diameter = 10 and the altitude/radius maximum is 5(as 10/2=5).

I didn't even try to solve it :3 because for any type of question, that answer is a common one! haha

the triangle i have given is impossible to be formed i gave the option as i can't find out to confuse you if i gave impossible triangle as a option every body could have had figured it out . more over for your information the max altitude of this triangle is 5 . (so 6 is impossible !!!)