Question

The hypotenuse of a right-angled triangle measures 6.5 m and its base measures 6 m. Find the length of perpendicular and hence, calculate the area of the triangle.

Answer 1

Hypotenuse = 6.5 m
​Base = 6 m
In a right-angled triangle,
$$\begin{gathered} {\left(\mathrm{Hypotenuse}\right)}^2={\left(\text{B}\mathrm{ase}\right)}^2+{\left(\text{P}\mathrm{erpendicular}\right)}^2 \\ \Rightarrow 6.5^2=6^2+{\left(\mathrm{perpendicular}\right)}^2 \\ \Rightarrow 6.5^2-6^2={\left(\mathrm{perpendicular}\right)}^2 \\ \Rightarrow {\left(\mathrm{perpendicular}\right)}^2=(6.5-6)(6.5+6) \\ \Rightarrow {\left(\mathrm{perpendicular}\right)}^2=0.5\times 12.5 \\ \Rightarrow {\left(\mathrm{perpendicular}\right)}^2=6.25 \\ \Rightarrow \mathrm{perpendicular}=2.5\mathrm{m} \end{gathered}$$

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

$$\begin{gathered} =\frac{1}{2}\times 6\times 2.5 \\ =7.5{\mathrm{m}}^2 \end{gathered}$$