Let \( H_1 : \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1 \) and \( H_2 : -\dfrac{x^2}{A^2} + \dfrac{y^2}{B^2} = 1 \) be two hyperbolas having length of latus rectums \( 15\sqrt{2} \) and \( 12\sqrt{5} \) respectively. Let their eccentricities be \( e_1 = \sqrt{\dfrac{5}{2}} \) and \( e_2 \) respectively. If the product of the lengths of their transverse axes is \( 100\sqrt{10} \), then \( 25e_2^2 \) is equal to \( \underline{\phantom{xxxx}} \).
