Let ABCD be a convex quadrilateral with AB = a, BC = b, CD = c and DA

1.	Let ABCD be a convex quadrilateral with AB = a, BC = b, CD = c and DA = d. Suppose a2 + b2 + c2 + d2 = ab + bc + cd + da, and the area of ABCD is 60 square units. If the length of one of the diagonals is 30 units, determine the length of the other diagonal.
Answer» a²+b²+c²+d² = 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.

Let ABCD be a convex quadrilateral with AB = a, BC = b, CD = c and DA = d. Suppose a2 + b2 + c2 + d2 = ab + bc + cd + da, and the area of ABCD is 60 square units. If the length of one of the diagonals is 30 units, determine the length of the other diagonal.

Answer»

a²+b²+c²+d² = 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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Let ABCD be a convex quadrilateral with AB = a, BC = b, CD = c and DA = d. Suppose a2 + b2 + c2 + d2 = ab + bc + cd + da, and the area of ABCD is 60 square units. If the length of one of the diagonals is 30 units, determine the length of the other diagonal.

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