Question

What is the value of m in the figure below?

Answer 1

Answer:  8.2 (choice B)

==========================================================

Explanation:

First we'll need the length of segment BD, which I'll call x for now. The similar triangles allow us to set up the proportion below to solve for x

AD/BD = BD/DC

13/x = x/4

13*4 = x^2

52 = x^2

x^2 = 52

x = sqrt(52)

Segment BD is exactly sqrt(52) units long.

------------

Now focus your attention on triangle BDC. We'll use the pythagorean theorem to find BC

(BD)^2 + (DC)^2 = (BC)^2

( sqrt(52) )^2 + ( 4 )^2 = ( m )^2

52 + 16 = m^2

68 = m^2

m^2 = 68

m = sqrt(68)

m = 8.2462 approximately

m = 8.2