Question

Find the area of a triangle whose sides are 5 cm, 12 cm and 13 cm. Also, find its shortest altitude.

Answer 1

Here,
5² + 12²
= 25 + 144
= 169
= 13².
Thus, the triangle is a right angled triangle.
So, the length of hypotenuse is 13 and the length of the perpendicular sides are 5 and 12.
Therefore, the length of its shortest altitude is 5.
Now
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{triangle}=\frac{1}{2}\times \mathrm{base}\times \mathrm{height} \\ =\frac{1}{2}\times 12\times 5 \\ =30\mathrm{sq}.\mathrm{units} \end{gathered}$$
Hence, the area of the required triangle is 30 sq. units.