Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BC = 9

and DC = 3, what is the length of AC?

Answer 1

Explanation:

the height BD is (using Pythagoras) :

BD² = CB² - CD² = 9² - 3² = 81 - 9 = 72

BD = sqrt(72)

the height to the Hypotenuse of a right-angled triangle is also the square root of the product of the segment lengths of the Hypotenuse (the segments created by point D).

so, BD = sqrt(3×(x-3))

therefore,

sqrt(72) = sqrt(3×(x-3))

72 = 3×(x-3) = 3x - 9

81 = 3x

x = 27