What is the value of m in the figure below in this diagram abd bcd

Mathematics

1 answer:

oee [108]3 years ago

6 0

$\triangle BCA\ \text{and}\ \triangle DCB\ \text{are similar (AAA). Therefore the sides are in proportion:}\\\\\dfrac{BC}{CD}=\dfrac{AC}{BC}\\\\\text{We have}\\\\BC=m\\CD=7\\AC=7+11=18\\\\\text{Substitute:}\\\\\dfrac{m}{7}=\dfrac{18}{m}\qquad\text{cross multiply}\\\\m^2=(7)(18)\\\\m^2=126\to\boxed{m=\sqrt{126}}\to\boxed{A.}$

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