Question

Construct a right triangle with given hypotenuse c such that the median
drawn to the hypotenuse is the geometric mean of the two legs of the triangle.

Answer 1

@Noemi95

Answer 2

@Koikkara

Answer 3

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Answer 4

Mr. Owl Help me

Answer 5

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Answer 6

@TessaMarie08181997 Genius girl help me.

Answer 7

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Answer 8

The conditions of the problem require that



However, we notice that twice the area of the triangle is , since and form a right angle. However, twice the area of the triangle is also the product of and the altitude to . Hence the altitude to must have length . Therefore if we construct a circle with diameter and a line parallel to and of distance from , either point of intersection between the line and the circle will provide a suitable third vertex for the triangle. Q.E.D.