Answer:
x = 9
Explanation:
You want the length of the hypotenuse in the right triangle with one hypotenuse segment of length 4 and altitude to the hypotenuse of length 2√5.
Geometric mean
The altitude of the triangle is the geometric mean of the segments of the hypotenuse:
2√5 = √(4·(x-4))
4·5 = 4·(x -4) . . . . . . square both sides
5 = x -4 . . . . . . . divide by 4
9 = x . . . . . . . add 4
The length of x is 9 units.
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