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Nice problem! After googling "hyperbolic triangles of equal area on a fixed base" I found the paper "Extremal properties of the principal Dirichlet eigenvalue for regular polygons in the hyperbolic plane" by Karp and Peyerimhoff. Their Theorem 7 looks like the result you ask for. In a footnote KP refer to a 1965 book of Fejes Toth, "Regulare Figuren", as containing the same result. There appears to be an English version "Regular Figures" published in 1964.

This question seems very interesting in spherical geometry, as well.
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Nice problem! After googling "hyperbolic triangles of equal area on a fixed base" I found the paper "Extremal properties of the principal Dirichlet eigenvalue for regular polygons in the hyperbolic plane" by Karp and Peyerimhoff. Their Theorem 7 looks like the result you ask for. In a footnote KP refer to a 1965 paper book of Toth, "Regulare Figuren" Figuren", as containing the same result. There appears to be an English version "Regular Figures" published in 1964.

This question seems very interesting in spherical geometry, as well.
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Nice problem! After googling "hyperbolic triangles of equal area on a fixed base" I found the paper "Extremal properties of the principal Dirichlet eigenvalue for regular polygons in the hyperbolic plane" by Karp and Peyerimhoff. Their Theorem 7 looks like the result you ask for. In a footnote KP refer to a 1965 paper of Toth "Regulare Figuren" as containing the same result.

This question seems very interesting in spherical geometry, as well.