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Omni-MATH / Pentagon JAMES is such that AM=SJ and the internal angles satisfy ∠J=∠A=∠E=90^(∘), and ∠M=∠S. Given that there exists a diagonal of JAMES that bisects its area, find the ratio of t…

Problem

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problem

Pentagon JAMESJ A M E S is such that AM=SJA M=S J and the internal angles satisfy ∠J=∠A=∠E=90∘\angle J=\angle A=\angle E=90^{\circ}, and ∠M=∠S\angle M=\angle S. Given that there exists a diagonal of JAMESJ A M E S that bisects its area, find the ratio of the shortest side of JAMESJ A M E S to the longest side of JAMESJ A M E S.
Plain-text mathematical notation (without MathML)
Pentagon JAMES is such that AM=SJ and the internal angles satisfy ∠J=∠A=∠E=90^(∘), and ∠M=∠S. Given that there exists a diagonal of JAMES that bisects its area, find the ratio of the shortest side of JAMES to the longest side of JAMES.
Original LaTeX notation
Pentagon $J A M E S$ is such that $A M=S J$ and the internal angles satisfy $\angle J=\angle A=\angle E=90^{\circ}$, and $\angle M=\angle S$. Given that there exists a diagonal of $J A M E S$ that bisects its area, find the ratio of the shortest side of $J A M E S$ to the longest side of $J A M E S$.

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Source and history

task_id
fd24c1f9-d622-588e-af87-3f05a06bf44c
task_key
test--fd24c1f9-d622-588e-af87-3f05a06bf44c
task_revision_id
1
config / split
/ test

Official source

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