| Assertion (A): \[\Delta ABC\tilde{\ }\Delta DEF\] such that \[ar(\Delta ABC)=36c{{m}^{2}}\]and \[ar(\Delta DEF)=49c{{m}^{2}}\] then, \[\text{AB}:\text{DE}=\text{6}:\text{7}\]. |
| Reason (R): If \[\Delta ABC\tilde{\ }\Delta DEF,\] then \[\frac{ar(\Delta ABC)}{ar(\Delta DEF)}=\frac{A{{B}^{2}}}{D{{E}^{2}}}=\frac{B{{C}^{2}}}{E{{F}^{2}}}=\frac{A{{C}^{2}}}{D{{F}^{2}}}\] |
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] Both assertion and reason are true and reason is the correct explanation of assertion. |
| \[\frac{ar(\Delta ABC)}{ar(\Delta DEF)}=\frac{A{{B}^{2}}}{D{{E}^{2}}}\] |
| \[\frac{36}{49}=\frac{A{{B}^{2}}}{D{{E}^{2}}}\Rightarrow \frac{AB}{DE}=\frac{6}{7}\] |
| \[AB:DE=6:7\] |
| So, both assertion and reason are correct and reason is correct explanation of assertion. |
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