Question

In an isosceles right angled triangle, the square of the longest side is 13.52m, find the perimeter of the triangle.

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ \mathrm{The}\mathrm{longest}\mathrm{side}\mathrm{is}\mathrm{hypotenuse}\mathrm{so} \\ {\mathrm{hypotenuse}}^2=13.52\mathrm{m} \\ \mathrm{Now}\mathrm{since}\mathrm{it}\mathrm{is}\mathrm{isosceles}\mathrm{right}\mathrm{angle}\mathrm{triangle} \\ \mathrm{base}=\mathrm{perpendicular} \\ {\mathrm{base}}^2+{\mathrm{perpendicular}}^2={\mathrm{hypotenuse}}^2 \\ 2{\mathrm{base}}^2=13.52\mathrm{m} \\ \mathrm{base}=\sqrt{6.76}=2.6=\mathrm{perpendicular} \\ \mathrm{Hence}\mathrm{perimeter}=\mathrm{base}+\mathrm{perpendicular}+\mathrm{hypotenuse} \\ =2\times 2.6+\sqrt{13.52} \\ =5.2+3.67 \\ =8.87\mathrm{m} \\ \mathrm{Regards} \end{gathered}$$