10th Class Mathematics Triangles Question Bank Case Based (MCQs) - Triangles

  • question_answer
    If the measures of sides AB, BC and DE are \[\text{15 m},\] \[\text{21 m},\] and \[\text{10 m}\] respectively, then measure of side EF is:

    A) \[\text{14 m}\]

    B) \[\frac{50}{7}\text{ m}\]

    C) \[\text{12 m}\]

    D) \[\text{7 m}\]

    Correct Answer: A

    Solution :

    As triangles ABC and DEF are similar, so their, sides are proportional.
    \[\therefore \,\,\,\,\,\,\,\,\,\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}\,\,\,\Rightarrow \,\,\frac{AB}{DE}=\frac{BC}{EF}\]\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\frac{15}{10}=\frac{21}{EF}\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\,EF=\frac{10\times 21}{15}=14\,m\]
    So, option [a] is correct.

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