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Question

The length of the longest diagonal of the parallelogram constructed on 5 stack a with rightwards arrow on top plus 2 stack b with rightwards arrow on top and stack a with rightwards arrow on top minus 3 stack b with rightwards arrow on top comma if it is given that vertical line stack a with rightwards arrow on top vertical line equals 2 square root of 2 comma vertical line stack b with rightwards arrow on top vertical line equals 3 and angle stack a with rightwards arrow on top comma stack b with rightwards arrow on top equals fraction numerator pi over denominator 4 end fraction comma is

  1. square root of 473  
  2. square root of 593  
  3. square root of 474  
  4. None of these  

The correct answer is: square root of 593


    one diagonal = 6 stack a with rightwards arrow on top – stack b with rightwards arrow on top
    vertical line 6 stack a with rightwards arrow on top – stack b with rightwards arrow on top vertical line = square root of 36 vertical line stack a with rightwards arrow on top vertical line to the power of 2 end exponent plus vertical line stack b with rightwards arrow on top vertical line to the power of 2 end exponent – 12 stack a with rightwards arrow on top. stack b with rightwards arrow on top end root
    = square root of 36 cross times 8 plus 9 – 12 cross times 2 square root of 2 cross times 3 cross times fraction numerator 1 over denominator square root of 2 end fraction end root equals 15
    second diagonal = 4 stack a with rightwards arrow on top plus 5 stack b with rightwards arrow on top
    vertical line 4 stack a with rightwards arrow on top plus 5 stack b with rightwards arrow on top vertical line = square root of 16 vertical line stack a with rightwards arrow on top vertical line to the power of 2 end exponent plus 25 vertical line stack b with rightwards arrow on top vertical line to the power of 2 end exponent plus   40 stack a with rightwards arrow on top. stack b with rightwards arrow on top end root
    = square root of 16 cross times 8 plus 25 cross times 9 plus 40 cross times 6 end root = square root of 593

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