Question

The dimensions of a rectangular field are $80\mathrm{m}$ and $18\mathrm{m}$. Find the length of its diagonal.

Answer 1

Determine the length of the diagonal.

It is known that the angle of the rectangle is $90°$. According to the given information, the figure will be:

The Pythagoras theorem states that, the square of the length of the diagonal is the sum of the squares of the length of the legs of the right angled triangle. Apply Pythagoras theorem to determine the length of diagonal:

$\begin{array}{rcl}{\mathrm{diagonal}}^2& =& {80}^2+{18}^2\\ & \Rightarrow & {\mathrm{diagonal}}^2=6400+324\\ & \Rightarrow & {\mathrm{diagonal}}^2=6724\\ & \Rightarrow & \mathrm{diagonal}=\sqrt{6724}\\ & \Rightarrow & \mathrm{diagonal}=82\\ & & \end{array}$

Hence, the length of the diagonal is $82\mathrm{m}$.