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  5. Congruence of Triangles

7th Class Mathematics Congruence of Triangles Question Bank Congruence of Triangles

  • question_answer
    Tiara wants to know the width of the given river. While doing so, she stands on the edge of the river and look straight across to a point on the other edge without changing the inclination of the neck and head. She turns side ways until the vision is in line with a point on the side of the stream. From the above description, find the value of QR.            

    A)  25 units

    B)  12 units

    C)  15 units

    D)  Can't be determined

    Correct Answer: C

    Solution :

    In \[\Delta PQS.\] \[P{{S}^{2}}=P{{Q}^{2}}+Q{{S}^{2}}\] \[{{17}^{2}}={{8}^{2}}+Q{{S}^{2}}\]or \[Q{{S}^{2}}=289-64\] \[\Rightarrow \]  \[Q{{S}^{2}}=225\text{ }\Rightarrow \text{ }QS=15\] from given conditions, \[RQ=OS\]  (By CPCT) \[(\because \,\Delta PQR=\Delta PQS)\] \[\therefore \] \[QR=15\] units.


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