In a right-angled triangle ABC through the middle P of leg AC, a perpendicular is drawn

In a right-angled triangle ABC through the middle P of leg AC, a perpendicular is drawn that intersects the hypotenuse AB at point M. Find AB if CM = 11 cm

Consider the segment PM.

Point P, according to the condition, is the middle of the leg AC, AP = CP, then the segment PM is the middle line of the triangle ABC and AM = BM.

Then the segment CM will be the median drawn from the vertex of the right angle to the hypotenuse.

By the property of the median drawn from the vertex of the right angle of the triangle, it is equal to half the length of the hypotenuse.

CM = AB / 2.

AB = 2 * CM = 2 * 11 = 22 cm.

Answer: The length of the hypotenuse AB = 22 cm.