2025 SSMO Team Round Problems/Problem 3

Problem

A rectangle is divided as shown into nine smaller rectangles. The areas of the five smallest rectangles are $1,$ $2,$ $3,$ $4,$ and $5$ . What is the largest possible area of the original rectangle? $[asy] unitsize(1cm); draw((0,0)--(4,0)--(4,3)--(0,3)--cycle); draw((1,0)--(1,3)); draw((1.7,0)--(1.7,3)); draw((0,0.8)--(4,0.8)); draw((0,2)--(4,2)); [/asy]$

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2025 SSMO Team Round Problems/Problem 3

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