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SSC Sample Paper Mock Test-17 SSC CGL Tear-II Paper-1

  • question_answer
    The perimeter of a rectangle and a square are 160 m each. The area of the rectangle is less than that of the square by 100 sq m. The length of the rectangle is

    A) 30 m

    B)  60 m

    C)  40 m

    D)  50 m

    Correct Answer: D

    Solution :

    Let the length and breadth of rectangle be x and y m, respectively. According to the question, \[2(x+y)=160\] \[\Rightarrow \]   \[x+y=\frac{160}{2}=80\,\,\text{m}\]                ?(i) Perimeter of square = 160 m \[\therefore \]      Side of square \[=\frac{160}{4}=40\,\,\text{m}\] Now, area of rectangle = xy Area of square \[=40\times 40=1600\,\,{{\text{m}}^{\text{2}}}\] Then,    \[1600-xy=100\] \[\Rightarrow \]   \[xy=1600-100=1500\]               ?(ii) Now,     \[{{(x-y)}^{2}}={{(x+y)}^{2}}-4xy\] \[={{(80)}^{2}}-4\times 1500\]   \[=6400-6000=400\]             \[\Rightarrow \]    \[x-y=\sqrt{400}=20\]              ?(iii) From Eqs. (i) and (iii), we get \[2x=100\]             \[\Rightarrow \]   \[x=\frac{100}{2}=50\,\,\text{m}\]


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