Let ABC a right triangle in A (BC is the hypotenuse).
From A, draw the altitude AH, intersecting the hypotenuse in H
In any right triangle , the square of the altitude AH is equal to BH x HC, then
AH² = BH x HC
60² = 36 x 100 = 3600 So BH = 36 and HC = 100 (and the altitude = 60)
Follow the same logic for the remaining questions.
NB ( you can easily demonstrate that AH² = BH x HB, if you notice that the right triangles ABH and CAH are similar)
AH is called the geometric mean
