+7 Shown below is rectangle $EFGH$. Its diagonals meet at $Y$. Let $X$ be the foot if an altitude is dropped from $E$ to $\overline{FH}$. If $EX = 24$ and $GY = 28$, find the perimeter of rectangle $EFGH$.
[asy] size(4 cm); real x = 3, y = 2; pair H = (0,0), EE = (0,y), F = (x,y), G = (x,0), Y = F / 2, X = F * y^2 / (x^2 + y^2); draw(H--EE--F--G--H--F); draw(EE--G); draw(EE--X); label("$H$",H,SW); label("$E$",EE,NW); label("$F$",F,NE); label("$G$",G,SE); label("$X$",X,SE); label("$Y$",Y,2N); draw(rightanglemark(EE,X,H,6)); [/asy]
