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10th Class Mathematics Triangles Question Bank MCQs - Triangles

  • question_answer
    In \[\Delta ABC,\] it is given that \[\text{AB}=\text{9cm},\]\[\text{BC}=\text{6cm}\]and \[\text{CA}=\text{7}.\text{5cm}\]. Also, \[\Delta DEF\] is given such that \[EF=8\,cm\]and\[\Delta DEF\tilde{\ }\Delta ABC\].Then, perimeter of \[\Delta DEF\] is:

    A) \[\text{22}.\text{5 cm}\]

    B) \[\text{25 cm}\]

    C) \[\text{27 cm}\]

    D) \[\text{30 cm}\]

    Correct Answer: D

    Solution :

    [d] Perimeter of
    \[\Delta ABC=(9+6+7.5)cm=22.5cm\]
    Let the perimeter of \[\Delta DEF\] be p cm.
    Given, \[\Delta DEF\tilde{\ }\Delta ABC\]
    \[\therefore \,\,\,\frac{\text{Perimeter of}\,\Delta \text{DEF}}{\text{Perimeter of}\,\,\Delta \text{ABC}}=\frac{EF}{BC}\,\,\,\Rightarrow \,\,\frac{P}{22.5}=\frac{8}{6}\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,p=\frac{22.5\times 8}{6}=\frac{225\times 8}{60}=30cm.\]


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