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9th Class Mathematics Triangles Question Bank Triangle

  • question_answer
    In the given figure below, ABC is a triangle, PQ is line segment intersecting AB in P and AC in Q and \[\mathbf{PQ}\parallel \mathbf{BC}\]. The ratio of AP: BP = 2:5 and length of PQ is 18 cm. The length of BC is

    A)  36 cm.                       

    B)  63 cm.

    C)  48 cm.                       

    D)  24 cm.

    Correct Answer: B

    Solution :

    (b): \[PQ\parallel BC\]             \[\therefore \] \[\angle APQ=\angle ABC\] \[\angle AQP=\angle ACB\] By AA - similarity theorem, \[\Delta APQ\sim \Delta ABC\] \[\therefore \]\[\frac{AB}{AP}=\frac{BC}{PQ}\] \[\Rightarrow \] \[\frac{AP-PQ}{AP}=\frac{BC-PQ}{PQ}\] \[\Rightarrow \]\[\frac{AB}{AP}=\frac{BC-PQ}{PQ}\] \[\Rightarrow \]\[\frac{5}{2}=\frac{BC-18}{18}\] \[\Rightarrow \]\[BC-18=\frac{5}{2}\times 18=45\] \[\Rightarrow \]\[BC=45+18=63\]cm


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