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Omni-MATH / Let a,b be positive reals with a>b>(1)/(2)a. Place two squares of side lengths a,b next to each other, such that the larger square has lower left corner at (0,0) and the smaller sq…

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problem

Let a,ba, b be positive reals with a>b>12aa>b>\frac{1}{2} a. Place two squares of side lengths a,ba, b next to each other, such that the larger square has lower left corner at (0,0)(0,0) and the smaller square has lower left corner at (a,0)(a, 0). Draw the line passing through (0,a)(0, a) and (a+b,0)(a+b, 0). The region in the two squares lying above the line has area 2013. If (a,b)(a, b) is the unique pair maximizing a+ba+b, compute ab\frac{a}{b}.
Plain-text mathematical notation (without MathML)
Let a,b be positive reals with a>b>(1)/(2)a. Place two squares of side lengths a,b next to each other, such that the larger square has lower left corner at (0,0) and the smaller square has lower left corner at (a,0). Draw the line passing through (0,a) and (a+b,0). The region in the two squares lying above the line has area 2013. If (a,b) is the unique pair maximizing a+b, compute (a)/(b).
Original LaTeX notation
Let $a, b$ be positive reals with $a>b>\frac{1}{2} a$. Place two squares of side lengths $a, b$ next to each other, such that the larger square has lower left corner at $(0,0)$ and the smaller square has lower left corner at $(a, 0)$. Draw the line passing through $(0, a)$ and $(a+b, 0)$. The region in the two squares lying above the line has area 2013. If $(a, b)$ is the unique pair maximizing $a+b$, compute $\frac{a}{b}$.

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Source and history

task_id
52cb2007-551d-5667-ada6-3e3233ae32b5
task_key
test--52cb2007-551d-5667-ada6-3e3233ae32b5
task_revision_id
1
config / split
/ test

Official source

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