Answer:
6.6
Explanation:
You want the segment length x of the hypotenuse of a right triangle that has long side 18 and an altitude dividing the hypotenuse into parts of 15 and x.
Geometric mean
The fact that these right triangles are all similar gives rise to three geometric mean relations. The one applicable here relates the long leg of the triangle to the hypotenuse segments:
long leg/hypotenuse = 18/(15+x) = 15/18
18² = 15(15 +x)
Solving for x, we find ...
18²/15 = 15 +x = 21.6
x = 6.6 . . . . . . . subtract 15
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Additional comment
Taking the square root of the expression we found above, we get the geometric mean relation:
18 = √(15(15 +x))
The long leg is the geometric mean of adjacent hypotenuse segment and the whole hypotenuse.