$48^2 = (50-r_2+x)(50+r_2-x) \Rightarrow r_2-x = 14 \Rightarrow x = r_2-14 ~~~~~~...(1)$
$r_2^2+x^2 = (50-r_2)^2 \Rightarrow r_2^2 + (r_2-14)^2=(50-r_2)^2 \Rightarrow (r_2-24)(r_2+96) = 0$
$r_2 = 24$
$r_1^2 + (r_1+r_2-x)^2=(50-r_1)^2 \Rightarrow r_1^2 + (r_1+14)^2 = (50-r_1)^2 \Rightarrow (r_1-16)(r_1+144) = 0$
$r_1 = 16$
$GH = r_1+r_2 = 16 + 24 = 40$