In the given figure, \[\angle ABC=90{}^\circ \]and \[BD\bot AC\]. If BD = 8 cm and AD = 4 cm, then the value of CD is |
A) 8 cm
B) 12cm
C) 14cm
D) 16cm
Correct Answer: D
Solution :
Given, BD = 8 cm and AD = 4 cm |
In \[\Delta ADB\] and \[\Delta BDC\], |
\[\angle BDA=\angle CDB\] [each \[90{}^\circ\]] |
\[\angle DBA=\angle DCB\] [each \[\left( 90{}^\circ -\angle A \right)\]] |
\[\therefore \Delta ADB\tilde{\ }\Delta BDC\] |
[by AA similarity criterion] |
\[\Rightarrow \,\,\,\frac{BD}{CD}=\frac{AD}{BD}\] |
(since, corresponding sides of similar triangles are proportional] |
\[\Rightarrow \,\,\,\,CD=\frac{B{{D}^{2}}}{AD}\] |
\[\therefore \,\,\,CD=\frac{{{8}^{2}}}{4}=\frac{64}{4}=16\,\,cm\] |
You need to login to perform this action.
You will be redirected in
3 sec