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NTSE Sample Paper NTSE SAT Practice Test-10

  • question_answer
    Triangles ABC and DEF are similar such that  \[\frac{AB}{DE}=\frac{BC}{EF}\]. The area of \[\Delta ABC\] is \[16\,c{{m}^{2}}\]And that of \[\Delta DEF\]is 49\[c{{m}^{2}}\]. If \[BC=2\sqrt{2}\] cm then what is EF equal to?    

    A) 3.5cm                          

    B) \[(3.5)\sqrt{2}cm\]

    C) \[(3.5)\sqrt{3}cm\]         

    D)        \[7.0cm\]

    Correct Answer: B

    Solution :

    [b] Since \[\Delta ABC~\sim \Delta DEF,\] \[\frac{\Delta ABC}{\Delta DEF}=\frac{B{{C}^{2}}}{E{{F}^{2}}}=\frac{16}{49}\] \[\therefore \,\,\,\,\frac{BC}{EF}=\frac{4}{7}\] Also, \[\frac{2\sqrt{2}}{EF}=\frac{4}{7}\,\,\Rightarrow \,\,EF=(3.5)\sqrt{2}\]  cm


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