2. Questions Bank
  3. 9th Class
  4. Mathematics
  5. Triangles

9th Class Mathematics Triangles Question Bank Triangle

  • question_answer
    In a \[\Delta \mathbf{ABC}\], X and Y are two points on PQ and PR respectively such that \[\mathbf{XY}\parallel \mathbf{QR}\], bisects the AABC in two equal areas. Then the ratio QX : PQ is

    A)  \[1:\sqrt{2}\]               

    B)  1:2

    C)  \[\left( \sqrt{2}-1 \right):\sqrt{2}\]   

    D)  \[\sqrt{2}:1\]

    Correct Answer: C

    Solution :

    (c): \[\Delta PXY=[\,\,\,\,\,\,\,\,]\,\,\,QXYR\]       (Given) \[\Rightarrow \]\[\Delta 2PXY=\Delta PQR\] \[XY\parallel QR\] \[\therefore \]\[\Delta PXY\sim \Delta PQR\] \[\therefore \]\[\frac{\Delta PXY}{\Delta PQR}=\frac{1}{2}=\frac{P{{X}^{2}}}{P{{Q}^{2}}}\] \[\Rightarrow \]\[\frac{PQ}{PX}=\sqrt{2}\] \[\Rightarrow \]\[\frac{PQ}{PX}-1=\sqrt{2}-1\] \[\therefore \]\[\frac{QX}{PQ}=\frac{QX}{PX}\times \frac{PX}{PQ}=\frac{\sqrt{2-1}}{\sqrt{2}}\]             


You need to login to perform this action.
You will be redirected in 3 sec spinner