It can be observed that the lengths of the altitudes of a 3-4-5 right triangle are, respec...

It can be observed that the lengths of the altitudes of a 3-4-5 right triangle are, respectively, 4, 3, and 2.4 = 12/5 units. (The altitude to the side of length 5 units is found by using the area formula A = bh.)

(a) Show that the reciprocals of these altitudes, and satisfy the Pythagorean relation c'2 = a'2 + b'2.

(b) Using the area formula for a right triangle in general, show that if h1, h2, and h3 are the altitudes to the sides of length a, b, and c, respectively, then