Answer:
x = 4
Step-by-step explanation:
In this geometry, all of the right triangles are similar. That means the ratio of short side to long side is the same for all of the right triangles:
x/10 = 10/25
x = 100/25 = 4 . . . . . multiply by 10
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Additional comment
You may notice that the two segments of the hypotenuse, x and 25, have a product that is the square of the altitude. Another way to say this is that the altitude is the geometric mean of the segments x and 25.
There are two other geometric mean relations in this geometry:
the short side at the right is the geometric mean of x and (x+25).
the long side at the bottom is the geometric mean of 25 and (25+x).
That is, the segments that intersect the hypotenuse are the geometric mean of the two segments of the hypotenuse that they meet.
geometric mean of A and B is √(AB)
