MathLabs

Problem 1

In a convex quadrilateral of area 3232, the sum of the lengths of two opposite sides and one diagonal is 1616. Determine all possible lengths of the other diagonal.
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In plain words

The diagonal splits the quadrilateral into two triangles.

AB+BD+DC=16AB+BD+DC=16
Detailed analysis

Label the convex quadrilateral so the given diagonal is BDBD and the given sum is AB+BD+DC=16AB+BD+DC=16. Let d1,d2d_1,d_2 be the altitudes from A,CA,C to line BDBD.