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

  • question_answer
    Direction: Q. 11 to 15
    Gaurav placed a light bulb at a point O on the ceiling and directly below it placed a table. He cuts a polygon, say a quadrilateral PQRS, from a plane cardboard and place this cardboard parallel to the ground between the lighted bulb and the table. Then a shadow of PQRS is cast on the table as P’Q’R’S. Quadrilateral P'Q'R'S' is an enlargement of the quadrilateral PQRS with scale factor \[\text{1}:\text{3}\] Given that \[\text{PQ}=\text{2}.\text{5cm},\] \[\text{QR}=\text{3}.\text{5 cm}\]. \[\text{RS}=\text{3}.\text{4 cm}\] and \[\text{PS}=\text{3}.\text{1 cm};\] \[\angle P=115{}^\circ ,\] \[\angle Q=95{}^\circ ,\] \[\angle R=65{}^\circ \]and \[\angle S=85{}^\circ \].    
    Based on the given information, give the answer of the following questions:
    The length of R'S' is:

    A) \[\text{3}.\text{4 cm}\]

    B) \[\text{1}0.\text{2 cm}\]

    C) \[\text{6}.\text{8 cm}\]

    D) \[\text{9}.\text{5 cm}\]

    Correct Answer: B

    Solution :

    Given, scale factor is \[1:3\]
    \[\therefore \,\,\,\,\,\,\,\,\,R'S'=3\times 3.4=10.2\,cm\]
    So, option [b] is correct.

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