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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