Question

In △ABC, BD is an altitude.



What is the length, in units, of BD?

5 square root 6

5

6 square root 5

9

Answer 1

BD looks like 15

Answer 2

nnot sure it is not drawn to scale

Answer 3

Let AB = x, BC =y and BD = z

Consider △ABC,
\(x^2+y^2 = (15+12)^2\)
\(x^2+y^2 = 27^2\) -(1)

Consider △BCD,
\(z^2 + 12^2 = y^2\) -(2)

Consider △ABD,
\(15^2 + z^2 = x^2\) -(3)

Put (2) and (3) into (1)
\((15^2 + z^2) + (z^2 + 12^2) = 27^2\)
\(2z^2 = 27^2 - 12^2 - 15^2\)
\(2z^2 = 360\)
\(z^2 = 180\)
\(z = \sqrt{180}\) or \(z = -\sqrt{180}\) (rejected)

So, \(BD =\sqrt{180} = ...?\)