The height of a right-angled triangle to the hypotenuse is 12 cm. Can the hypotenuse be equal to 20 cm?

The hypotenuse AB is the diameter of the circle circumscribed about the triangle ABC. The height of CH is half the length of the chord, which cannot be greater than the diameter AB, and since 12 * 2 = 24, and 24> 20, the hypotenuse cannot have a length of 20 cm.
Answer: It cannot.



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