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9th Class Mathematics Triangles Question Bank Triangle

  • question_answer
    A\[\Delta \mathbf{DEF}\] is formed by joining the mid-points of the sides of \[\Delta \mathbf{ABC}\]. Similarly, a \[\Delta \mathbf{DEF}\] is formed by joining the mid-points of the sides of the \[\Delta \mathbf{PQR}\]. If the sides of the \[\Delta \mathbf{PQR}\] are of lengths 2, 3 and 4 units, what is the perimeter of the\[\Delta \mathbf{ABC}\]?

    A)  18 units                       

    B)  36 units

    C)  48 units                       

    D)  cannot be determined

    Correct Answer: B

    Solution :

    (b): Perimeter of \[\Delta PQR=2+3+4=9\]units Now, in \[\Delta DEF\], \[\frac{DQ}{DF}=\frac{1}{2}=\frac{PQ}{FE}\] So, \[2PQ=FE\] Similarly,     \[DF=2PR\] and \[DE=2QR\] \[\therefore \]Perimeter of \[\Delta DEF=2\times 9=18\]units Similarly, perimeter of \[\Delta ABC=2\times Perimeter\text{ }of\text{ }\Delta DEF\] \[=2\times 18\] \[=36\]units


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