What is the value of m in the figure below? If necessary, round your answer to the nearest tenth of a unit. A. 18 B. 13.2 C. 12.5 D. 7

1 answer
Question:

What is the value of m in the figure below? If necessary, round your answer to
the nearest tenth of a unit.
A. 18
B. 13.2
C. 12.5
D. 7

Answers

First [tex]\\ \sf\longmapsto BD^2=AD\times DC[/tex] [tex]\\ \sf\longmapsto BD^2=18^2+7^2[/tex] [tex]\\ \sf\longmapsto BD^2=324+49[/tex] [tex]\\ \sf\longmapsto BD^2=363[/tex] [tex]\\ \sf\longmapsto BD=\sqrt{363}[/tex] [tex]\\ \sf\longmapsto BD=19.2[/tex]NowUsing Pythagorean theorem [tex]\\ \sf\longmapsto BD^2+CD^2=m^2[/tex] [tex]\\ \sf\longmapsto m^2=7^2+19.2^2[/tex] [tex]\\ \sf\longmapsto m^2=49+363[/tex] [tex]\\ \sf\longmapsto m^2=412[/tex] [tex]\\ \sf\longmapsto m=\sqrt{412}[/tex] [tex]\\ \sf\longmapsto m=20.3[/tex]Nearest value in options is 18 Hence option a is correct

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