| 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] |
| \[\Rightarrow \,\,\,\,CD=\frac{B{{D}^{2}}}{AD}\] |
| \[\therefore \,\,\,CD=\frac{{{8}^{2}}}{4}=\frac{64}{4}=16\,\,cm\] |
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