A) 4:5
B) 5:4
C) 3:2
D) 5:7
Correct Answer: A
Solution :
[a] |
Let \[\Delta ABC\]and \[\Delta PQR\] be two isosceles triangles such that \[\angle A=\angle P,\] \[\angle B=\angle Q\] and \[\angle C=\angle R\] |
\[\therefore \,\,\,\Delta ABC\tilde{\ }\Delta PQR\] |
(By AAA similarity criterion) |
Let AD and PS be the altitudes of \[\Delta ABC\] and \[\Delta PQR\]respectively, |
Since, ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding altitudes. |
\[\therefore \,\,\,\,\,\,\,\frac{ar(\Delta ABC)}{ar(\Delta PQR)}={{\left( \frac{AD}{PS} \right)}^{2}}\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\frac{16}{25}={{\left( \frac{AD}{PS} \right)}^{2}}\,\,\,\Rightarrow \,\,\,\frac{AD}{PS}=\frac{4}{5}\] |
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