| Assertion (A): ABC and DEF are two similar triangles such that \[\text{BC}=\text{4cm},\] \[\text{EF}=\text{5cm}\] and area of \[\Delta ABC=64\,c{{m}^{2}},\] then area of \[\Delta DEF=100\,c{{m}^{2}}\]. |
| Reason (R): The areas of two similar triangles are in the ratio of the squares of the 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: B
Solution :
| [b] It both assertion and reason are correct, buit reason is not the correct explanation of assertion. |
| Reason is true. (standard result] |
| For assertion, since \[\Delta ABC\tilde{\ }\Delta DEF\] |
| \[\frac{ar(\Delta ABC)}{ar(\Delta DEF)}=\frac{B{{C}^{2}}}{E{{F}^{2}}}=\frac{{{(4)}^{2}}}{{{(5)}^{2}}}=\frac{16}{25}\] |
| (ratio of areas of two similar triangles is equal to the ratio of the squares of corresponding sides) |
| \[\frac{64}{ar\,(\Delta DEF)}=\frac{16}{25}\] |
| \[ar(\Delta DEF)=\frac{64\times 25}{16}=4\times 25=100\,c{{m}^{2}}\] |
| Assertion is true but reason is not correct explanation of assertion. |
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