Question

What is the value of m in the figure below? If necessary, round your answer to

the nearest tenth of a unit.
A. 8.5
B. 8.2
C. 13
D. 4

Answer 1

B. 8.2

Explanation:

`In\: \triangle ABC, \:\angle ABC= 90\degree \: \&\: BD\perp AC`

So, by geometric mean property.

`BD = \sqrt {AD* CD} \\</p><p>BD = \sqrt {13* 4}\\</p><p>BD = \sqrt {52}\\</p><p>Next\: in \: \triangle BDC, \:\\</p><p>By\: Pythagoras \: theorem \\</p><p>m^2 = BD^2 + CD^2 \\</p><p>m^2 = (\sqrt {52}) ^2 + (4)^2 \\</p><p>m^2 =52 + 16\\</p><p>m^2 =68\\</p><p>m =√(68) \\</p><p>m = 8.24621125\\</p><p>m = 8.2`