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Exercise 3. Two medians of a triangle equal 9 and 12 and are perpendicular to each other. Calculate the length of the third median.Solution. We start drawing the triangle by drawing two mutually perpendicular straight lines. Then, towards the opposite sides from the intersection point O, we mark segments whose lengths satisfy a ratio of 2 to 1. Next we complete triangle ABC.The next step is to prove that ВН and АР are the triangle’s medians. Then we apply the properties of a triangle’s medians and find the lengths of segments
and
.In right-angled triangle АОВ, we find the length of hypotenuse АВ:
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