| In the given figure, the side PQ of a right triangle \[\Delta PQR\]where \[\text{OP}=\text{6 cm},\] \[\text{OR}=\text{8 cm}\] and \[\text{QR}=\text{26 cm},\]is : |
 |
A) \[21\,cm\]
B) \[23\,cm\]
C) \[24\,cm\]
D) \[36\,cm\]
Correct Answer: C
Solution :
| Applying Pythagoras theorem in triangle POR, we get, |
| \[P{{R}^{2}}=O{{P}^{2}}+O{{R}^{2}}={{6}^{2}}+{{8}^{2}}=1000\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,PR=10cm\] |
| Now, the apply Pythagoras theorem in triangle PQR. |
| \[Q{{R}^{2}}=P{{Q}^{2}}+P{{R}^{2}}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,{{26}^{2}}=P{{Q}^{2}}+{{10}^{2}}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,P{{Q}^{2}}={{26}^{2}}-{{10}^{2}}=676-100=576\] |
| Therefore, \[\text{PQ}=\text{24 cm}\]. |
| So, option [c] is correct |
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