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.
Solution:
Hypotenuse = 65 cm
Base = 60 cm
In a right-angled triangle,
$(\text { Hypotenuse })^{2}=(\text { B ase })^{2}+(\text { P erpendicular })^{2}$
$\Rightarrow(65)^{2}=(60)^{2}+(\text { perpendicular })^{2}$
$\Rightarrow(65)^{2}-(60)^{2}=(\text { perpendicular })^{2}$
$\Rightarrow(\text { perpendicular })^{2}=(65-60)(65+60)$
$\Rightarrow(\text { perpendicular })^{2}=5 \times 125$
$\Rightarrow(\text { perpendicular })^{2}=625$
$\Rightarrow$ perpendicular $=25 \mathrm{~cm}$
Area of triangle $=\frac{1}{2} \times$ base $\times$ perpendicular
$=\frac{1}{2} \times 60 \times 25$
$=750 \mathrm{~cm}^{2}$