A projectile can have same range from two angles of projection with same initial speed. If $h_1$ and $h_2$ be the maximum heights, then R will be?

$$\begin{gathered} \text{Range }R=\frac{u^2\sin 2\theta }{g} \text{ is same for angles }\theta \text{ and }90°-\theta . \\ \text{Maximum height for θ, }{h}_1=\frac{u^2{\sin }^2\theta }{2g} \\ \text{Maximum height for 90°-θ, }{h}_2=\frac{u^2{\sin }^2\left(90°-\theta \right)}{2g}=\frac{u^2{\cos }^2\theta }{2g} \\ \text{∴ }{h}_1{h}_2={\left(\frac{u^2·2\sin \theta \cos \theta }{g}\right)}^2·\frac{1}{4}·\frac{1}{4}={\left(\frac{u^2\sin 2\theta }{g}\right)}^2·\frac{1}{16}=\frac{R^2}{16} \\ \text{or, }R=4\sqrt{h_1{h}_2} \end{gathered}$$