What are the values of x and y?
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(the link is the picture that goes with the question)
In any right-angled triangle, if you draw a line from the 90° angle
to the hypotenuse and that line is perpendicular to the hypotenuse,
then the square of that line is equal to the product of the two segments on
the hypotenuse.
This can be easily shown by using ratios of sides of the similar triangles created.
in your case: 9^2 = 12x
x = 81/12 = 27/4
then AC = 12 + 27/4 = 75/4
lastly:
y^2 + 15^2 = (75/4)^2
y^2 = 2025/16
y = 45/4