Question

Given right triangle A, B, CABC with altitude start overline, B, D, end overline
BD
drawn to hypotenuse start overline, A, C, end overline
AC
. If A, C, equals, 22AC=22 and D, C, equals, 3, commaDC=3, what is the length of start overline, B, C, end overline
BC
in simplest radical form?

Answer 1

Drop of altitude to hypotenuse gives the geometric-mean relation BC^2 = AC·DC. Here AC = 22 and DC = 3, so BC^2 = 22·3 = 66. Hence BC = √66.