A rectangular mat has an area of 120 m² and perimeter of 46 The length of its diagonal is :

  1. 17 cm
  2. 27 m
  3. 17 mm²
  4. 17 m
Anurag Mishra Professor Asked on 26th January 2016 in Maths.
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  • 1 Answer(s)

    Answer:  (4) 17 m

    Solution:-
    Lat the length of the rectangle be L cm and width of the rectangle be B cm.

    The area of the rectangular mat = 120 
    Then L B = 120  …………….. (1) 

    The perimeter of the rectangular mat = 46
    Then,   2 (L + B) = 46
    L + B = 46/2
    L + B = 23 
    Square on both side, 
    (L + B)^2 = 23^2
    L^2 + B^2 + 2 x L B = 23 x 23 
    L^2 + B^2 + 2 x 120 = 529
    L^2 + B^2 = 529 – 240 
    L^2 + B^2 = 289
    Square root on both side, 
    (L^2 + B^2)^1/2  =17 

    Then, diagonal of the rectangle is 17 cm .

    Hence, the correct answer is option (4) 17 cm.

    Anurag Mishra Professor Answered on 26th January 2016.
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