Range of projectile, $R=\frac{2 u^{2} \sin \theta \cos \theta}{g}$ ...(i)
Height $H=\frac{u^{2} \sin ^{2} \theta}{2 g}$ ...(ii)
$H_{1}=\frac{u^{2} \sin ^{2}\left(90^{\circ}-\theta\right)}{2 g}=\frac{u^{2} \cos ^{2} \theta}{2 g}$ ...(iii)
Then, $H H_{1}=\frac{u^{2} \sin ^{2} \theta u^{2} \cos ^{2} \theta}{2 g 2 g}$ ...(iv)
From E (i),
we get $R^{2}=\frac{4 u^{2} \sin ^{2} \theta u^{2} \cos ^{2} \theta \times 4}{2 g 2 g}$ $R=\sqrt{16 H H_{1}}$
[from E (iv)] $=4 \sqrt{H H_{1}}$