Find the Length of a Diagonal (in cm) :

The area of an isosceles trapezium is 176 cm2 and the height is 2/11th of the sum of its parallel sides. If the ratio of the length of the parallel sides is 4:7, then the length of a diagonal (in cm) is

  1. 28
  2. √137
  3. 24
  4. 2√137
Anurag Mishra Professor Asked on 26th October 2015 in Maths.
Add Comment
  • 1 Answer(s)

    Answer: (4)  2(137)1/2 cm

    Explanation:-
    s = sum of parallel sides 
    h = height = 2s/11 

    V = 176 
    (2s/11) x s/2 = 176 
    s2/11 = 176 
    s2= 11 x 176
    = 1936 
    s = 44 cm

    Ratio of parallel sides =  4:7 
    Shorter parallel side = 4 x 44/11
    4 x 4 = 16 
    Longer parallel side = 7 x 44/11
     7 x 4 = 28 

    Now
    So, 28−16 = 12 and 12/2 = 6 
    So longer parallel base sticks out 6 cm more than shorter base at each end. 
    Draw a figure
     

    RE: Find the Length of a Diagonal (in cm) :


    Vertical distance from one end of diagonal to the other
     h = 2 x 44/11
     2 x 4 = 8 
    Horizontal distance from end of diagonal to the other = 16+6
     = 22 cm

    d2 = (82 + 222)1/2
         = (64 + 484)1/2
         = (5481/2 
    d = 2(137)1/2 cm

    Hence, the answer is (4)  2(137)1/2 cm.

    Monis Rasool Professor Answered on 28th October 2015.
    Add Comment
  • Your Answer

    By posting your answer, you agree to the privacy policy and terms of service.