The room
Red line is the diagonal, if we take the diagonal and the two sides below the square we havea right triangle
where h is the length of the diagonal or the hypotenuse of the triangle
we can use pythagoras to solve this right triangle
[tex]a^2+b^2=h^2[/tex]
where a and b are the sides of the triangle and h the hypotenuse
now replacing
[tex]\begin{gathered} 45^2+40^2=h^2 \\ \end{gathered}[/tex]
and simplify
[tex]\begin{gathered} 2025+1600=h^2 \\ 3625=h^2 \end{gathered}[/tex]
then solve for h
[tex]\begin{gathered} h=\sqrt[]{3625} \\ h=5\sqrt[]{145}\approx60.2 \end{gathered}[/tex]
then, the rounded lenght of the diagonal is 60ft
