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Omni-MATH / Let ABC be a triangle with AB=5,BC=4 and AC=3. Let P and Q be squares inside ABC with disjoint interiors such that they both have one side lying on AB. Also, the two squares each h…

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problem

Let ABCABC be a triangle with AB=5,BC=4AB=5, BC=4 and AC=3AC=3. Let P\mathcal{P} and Q\mathcal{Q} be squares inside ABCABC with disjoint interiors such that they both have one side lying on ABAB. Also, the two squares each have an edge lying on a common line perpendicular to ABAB, and P\mathcal{P} has one vertex on ACAC and Q\mathcal{Q} has one vertex on BCBC. Determine the minimum value of the sum of the areas of the two squares.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=5,BC=4 and AC=3. Let P and Q be squares inside ABC with disjoint interiors such that they both have one side lying on AB. Also, the two squares each have an edge lying on a common line perpendicular to AB, and P has one vertex on AC and Q has one vertex on BC. Determine the minimum value of the sum of the areas of the two squares.
Original LaTeX notation
Let $ABC$ be a triangle with $AB=5, BC=4$ and $AC=3$. Let $\mathcal{P}$ and $\mathcal{Q}$ be squares inside $ABC$ with disjoint interiors such that they both have one side lying on $AB$. Also, the two squares each have an edge lying on a common line perpendicular to $AB$, and $\mathcal{P}$ has one vertex on $AC$ and $\mathcal{Q}$ has one vertex on $BC$. Determine the minimum value of the sum of the areas of the two squares.

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Source and history

task_id
668d3976-23e6-5b20-bb1e-ac38a70fe31b
task_key
test--668d3976-23e6-5b20-bb1e-ac38a70fe31b
task_revision_id
1
config / split
/ test

Official source

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