9th Class Mathematics Areas of Parallelograms and Triangles Question Bank Area of Parallelogram & Triangle

  • question_answer The area of a rectangle lies between 40\[\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}\] and 45\[\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}\]. If one of the sides is 5cm, then its diagonal lies between

    A)  8 cm and 10 cm        

    B)  9 cm and 11 cm

    C)  10 cm and 12 cm         

    D)  11 cm and 13 cm

    Correct Answer: B

    Solution :

    (b):- Area of rectangle lies between 40\[c{{m}^{2}}\] and 45\[c{{m}^{2}}\] Now one side = 5 cm Since, area cannot be less than 40\[c{{m}^{2}}\] \[\therefore \]Other side cannot be less than \[=\frac{40}{5}=8\] cm Since, area cannot be greater than 45\[c{{m}^{2}}\] \[\therefore \]Other side cannot be greater than \[=\frac{45}{5}=9\]cm \[\therefore \]Minimum value of diagonal \[=\sqrt{{{8}^{2}}+{{5}^{2}}}\] Maximum value of diagonal \[=\sqrt{{{9}^{2}}+{{5}^{2}}}\]                                          \[=\sqrt{106}=10.3\]cm So, diagonal lies between 9 cm and 11 cm

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