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Answer:
x = √70
Step-by-step explanation:
The triangles shown are all similar, so corresponding sides are proportional.
hypotenuse/long side = x/7 = (7+3)/x
Cross-multiplying gives ...
x^2 = 7(10)
x = √70
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You will note that the value of x (the long side) is the geometric mean of the long segment and the whole hypotenuse.
A similar "geometric mean" relation holds for the short side:
BC = √(CD·CA)
There is yet another "geometric mean" relation that holds for the altitude:
BD = √(CD·AD)
You may see these again.
