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, 44AC=44 and D, C, equals, 28, commaDC=28, what is the length of start overline, B, C, end overline
BC
in simplest radical form?

Answer 1

Since BD is the altitude to hypotenuse AC, the altitude-to-hypotenuse theorem gives
BC^2 = DC · AC = 28 · 44 = 1232.
Thus BC = sqrt(1232) = sqrt(16·77) = 4√77.