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8th Class Mathematics Linear Equations in One Variable Question Bank Linear equations in One Variable

  • question_answer
    The perimeter of a rectangle is numerically equal to the area of rectangle. If width of rectangle is \[\text{2}\frac{3}{4}cm\], then its length is_____.

    A)  \[\frac{11}{3}cm\]    

    B)         \[\frac{22}{3}cm\]    

    C)         \[11cm\]         

    D)         \[10cm\]                     

    Correct Answer: B

    Solution :

    Let the length of rectangle be \[x\text{ }cm\]. Width of rectangle\[=2\frac{3}{4}cm=\frac{11}{4}cm\] \[\therefore \]Area of rectangle=length\[\times \]width                         \[=x\times \frac{11}{4}=\frac{11x}{4}sq.\,\,cm\] Also, perimeter of rectangle                         = 2(length + width) Now, according to question. \[\frac{11x}{4}=2x+\frac{11}{2}\Rightarrow \frac{11x}{4}-2x=\frac{11}{2}\] \[\Rightarrow \frac{11x-8x}{4}=\frac{11}{2}\Rightarrow \frac{3x}{4}=\frac{11}{2}\] \[\Rightarrow 6x=4\times 11\Rightarrow x=\frac{4\times 11}{6}=\frac{22}{3}cm\]


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