A) \[\frac{1}{2}\]
B) \[\frac{2}{1}\]
C) \[\frac{1}{3}\]
D) \[\frac{2}{3}\]
Correct Answer: A
Solution :
(a): From \[\Delta ABC\] \[AC=\sqrt{A{{B}^{2}}+B{{C}^{2}}}\] \[=\sqrt{A{{B}^{2}}+B{{C}^{2}}}\] \[~=\sqrt{2}BC\] \[\Delta QBC\parallel \Delta PAC\] \[\therefore \]\[\frac{Area\text{ }of\text{ }\Delta QBC}{Area\text{ }of\text{ }\Delta PAC\text{ }}\text{=}\frac{B{{C}^{2}}}{A{{C}^{2}}}\] \[=\frac{B{{C}^{2}}}{{{\left( \sqrt{2}BC \right)}^{2}}}\] \[=\frac{B{{C}^{2}}}{2B{{C}^{2}}}=\frac{1}{2}\]You need to login to perform this action.
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