| Assertion (A): The sum of the distances of \[\text{A}{{\text{D}}^{\text{2}}}+\text{B}{{\text{D}}^{\text{2}}}+\text{B}{{\text{E}}^{\text{2}}}+\text{C}{{\text{E}}^{\text{2}}}\]is\[\text{28}.\text{36}\]. |
| Reason (R): In right angled triangle, \[{{(Hypotenuse)}^{2}}={{(Perpendicular)}^{2}}+{{(Base)}^{2}}\]. |
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A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
Correct Answer: A
Solution :
| [a] Clearly, reason is true. |
| Now, in right \[A{{D}^{2}}=A{{M}^{2}}+D{{M}^{2}}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,A{{D}^{2}}={{(1.8)}^{2}}+{{(2)}^{2}}=3.24+4=7.24\] |
| In right \[\Delta DNB,\] \[D{{B}^{2}}=D{{N}^{2}}+B{{N}^{2}}\] |
| \[\Rightarrow \,\,\,\,\,D{{B}^{2}}={{(1.6)}^{2}}+{{2}^{2}}=2.56+4=6.56\] |
| In right \[\Delta EOB,\] |
| \[B{{E}^{2}}=O{{E}^{2}}+O{{B}^{2}}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,B{{E}^{2}}={{(1.6)}^{2}}+{{2}^{2}}=6.56\] |
| In right \[\Delta CPE,\] \[C{{E}^{2}}=C{{P}^{2}}+P{{E}^{2}}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,C{{E}^{2}}={{2}^{2}}+{{2}^{2}}=4+4=8\] |
| \[\therefore \,A{{D}^{2}}+B{{D}^{2}}+B{{E}^{2}}+C{{E}^{2}}=7.24+6.56+6.56+8=28.36\]\[\therefore \] Assertion: True; Reason: True and it is the correct explanation of assertion. |
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