| Assertion (A): In two similar triangles ABC and PQR, if their corresponding altitudes AD and PS are in the ratio \[\text{4}:\text{9},\] then the ratio of the areas of \[\Delta ABC\] and \[\Delta PQR\] is \[\text{16}:\text{81}\] |
| Reason (R): The ratio of the areas of two similar triangles is equal to the ratio of their corresponding altitudes. |
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: C
Solution :
| [c] Clearly, reason is false. |
| Since the ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding altitudes. |
| \[\therefore \,\,\,\,\,\,\,\,\,\frac{ar\,\,(\Delta ABC)}{ar\,\,(\Delta PQR)}=\frac{A{{D}^{2}}}{P{{S}^{2}}}\] |
| \[\Rightarrow \,\,\,\,\frac{ar\,\,(\Delta ABC)}{ar\,\,(\Delta PQR)}={{\left( \frac{4}{9} \right)}^{2}}=\frac{16}{81}\]\[[AD:PS=4:9]\] |
| Hence, \[ar(\Delta ABC):ar(\Delta PQR)=16:81\] |
| \[\therefore \] Assertion; True; Reason: False, |
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