Question

The hypotenuse of a right-angled triangle measures 65 cm and its base is 60 cm. Find the length of perpendicular and the area of the triangle.

Answer 1

Hypotenuse = 65 cm
​Base = 60 cm
In a right-angled triangle,
$$\begin{gathered} {\left(\mathrm{Hypotenuse}\right)}^2={\left(\text{B}\mathrm{ase}\right)}^2+{\left(\text{P}\mathrm{erpendicular}\right)}^2 \\ \Rightarrow {\left(65\right)}^2={\left(60\right)}^2+{\left(\mathrm{perpendicular}\right)}^2 \\ \Rightarrow {\left(65\right)}^2-{\left(60\right)}^2={\left(\mathrm{perpendicular}\right)}^2 \\ \Rightarrow {\left(\mathrm{perpendicular}\right)}^2=(65-60)(65+60) \\ \Rightarrow {\left(\mathrm{perpendicular}\right)}^2=5\times 125 \\ \Rightarrow {\left(\mathrm{perpendicular}\right)}^2=625 \\ \Rightarrow \mathrm{perpendicular}=25\mathrm{cm} \end{gathered}$$​

Area of triangle = $\frac{1}{2}\times \mathrm{base}\times \mathrm{perpendicular}$

$$\begin{gathered} =\frac{1}{2}\times 60\times 25 \\ =750{\mathrm{cm}}^2 \end{gathered}$$