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Let ABCD be a convex quadrilateral with AB = a, BC = b, CD = c and DA = d. Suppose and the area of ABCD is 60 square units. If the length of one of the diagonals is 30 unit, determine the length of the other diagonal.

  1. Let ABCD be a convex quadrilateral with AB = a, BC = b, CD = c and DA = d. Suppose a^2 + b^2 + c^2 + d^2 = ab + bc + cd + da  and the area of ABCD is 60 square units. If the length of one of the diagonals is 30 unit, determine the length of the other diagonal.

Grade:11

2 Answers

Saurabh Koranglekar
askIITians Faculty 10336 Points
2 years ago
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Vikas TU
14149 Points
2 years ago
a^2+b^2+c^2+d^2 = ab+bc+cd+da ) (a - b)2+(b - c)2+(c - d)2+(d - a)2 = 0 ) a = b = c = d.   Thus ABCD is a rhombus and   [ABCD] = (1/2)(d1d2) .....(1) where d1 and d2 are the lengths of the diagonals. Hence d2 = (2[ABCD])/d1 = 4units.

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