Answer:
x = 6.3
Step-by-step explanation:
The altitude divides the right triangle into two other right triangles, all of which are similar to the large one. Then the ratio of long side to short side is the same for the smaller two triangles:
... 10/x = x/4
... 40 = x^2 . . . . . multiply by the product of the denominators
... x = √40 ≈ 6.3 . . . . take the square root
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<em>Comment on the problem</em>
You can see that the altitude is the square root of the product of the hypotenuse lengths either side of it. The n-th root of the product of n numbers is called their "geometric mean." So, the value of x is the geometric mean of 10 and 4, the lengths of the parts of the hypotenuse.
This little tidbit can be useful to remember (at least while you're faced with this sort of problem).
