Question

In an isosceles triangle, the length of hypotenuse is 4 root 2. the length of each of its equal side is-

Answer 1

$$\begin{gathered} \mathrm{Considering}\mathrm{it}\mathrm{is}\mathrm{an}\mathrm{isosceles}\mathrm{right}\mathrm{angled}\mathrm{triangle}. \\ \mathrm{Let}\mathrm{the}\mathrm{measure}\mathrm{of}\mathrm{equal}\mathrm{sides}\mathrm{be}\mathrm{x}. \\ \mathrm{Applying}\mathrm{Pythagoras}\mathrm{theorem}, \\ {\left(\mathrm{Hypotenuse}\right)}^2={\left(\mathrm{Perpendicular}\right)}^2+{\left(\mathrm{Base}\right)}^2 \\ {\left(4\sqrt{2}\right)}^2={\mathrm{x}}^2+{\mathrm{x}}^2 \\ 32=2{\mathrm{x}}^2 \\ {\mathrm{x}}^2=16 \\ \mathrm{x}=4. \\ \mathrm{Length}\mathrm{of}\mathrm{each}\mathrm{of}\mathrm{its}\mathrm{equal}\mathrm{side}\mathrm{is}4\mathrm{unit}. \end{gathered}$$