Question

If the projections of a line segment on the coordinates axes are 3, 4 and 5 then its length is equal to ____________.

Answer 1

Since coordinates of a line segment from coordinate axes are 3, 4 and 5 then length is given by
$\sqrt{{\left(3-0\right)}^2+{\left(4-0\right)}^2+{\left(5-0\right)}^2}$
$$\begin{gathered} =\sqrt{9+16+25} \\ =\sqrt{25+25} \\ =\sqrt{50} \\ =\sqrt{5\times 2\times 5} \end{gathered}$$
$\mathrm{i}.\mathrm{e}\mathrm{length}\mathrm{is}5\sqrt{2}$