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.
Step 2 of 7: Write the area
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In plain words

Base-times-height turns geometry into an inequality.

Area=BD(d1+d2)2\mathrm{Area}=\frac{BD(d_1+d_2)}2
Detailed analysis

Splitting along BDBD gives Area=BD(d1+d2)2\mathrm{Area}=\frac{BD(d_1+d_2)}2.