<s>[INST] The side lengths of a right-angled triangle of base $b$, height $h$, and hypotenuse $c$ form a Pythagorean triple, with $b < h < c$. The area of the triangle, $A$, is given by $A = \frac{1}{2}bh$. The area is also given by an isosceles triangle with side lengths $a$, $a$, and $d$, where $a > d$, and the angle between the two equal sides is $60^\circ$. For this triangle, the area is $A = \frac{\sqrt{3}}{4}a^2$. What is the value of $a$ in terms of $b$ and $h$?[/INST]