| Assertion (A): \[\Delta ABC\tilde{\ }\Delta DEF\] such that \[ar(\Delta ABC)=100c{{m}^{2}}\]and \[ar(\Delta DEF)=144c{{m}^{2}}\]. If \[\text{AB}=\text{24 cm},\]then \[\text{DE}=\text{36 cm}\]. |
| Reason (R): The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding medians |
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: D
Solution :
| [d] Clearly, reason is true, |
| Now, we know that, ratio of area of two similar triangles is equal to the ratio of squares of their corresponding sides. |
| \[\therefore \,\,\,\,\,\,\frac{ar(\Delta ABC)}{ar(\Delta DEF)}=\frac{A{{B}^{2}}}{D{{E}^{2}}}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\frac{100}{144}=\frac{24\times 24}{D{{E}^{2}}}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,D{{E}^{2}}=\frac{24\times 24\times 144}{100}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,DE=\frac{24\times 12}{10}=\frac{288}{10}=28.8\ne 36\] |
| \[\therefore \] Assertion : False; Reason : True, |
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