Question

The dimensions of a room are 45 ft by 40 ft, respectively. Find the length across the diagonal of the room to the nearest whole number.

Answer 1

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

`a^2+b^2=h^2`

where a and b are the sides of the triangle and h the hypotenuse

now replacing

`\begin{gathered} 45^2+40^2=h^2 \\ \end{gathered}`

and simplify

`\begin{gathered} 2025+1600=h^2 \\ 3625=h^2 \end{gathered}`

then solve for h

`\begin{gathered} h=\sqrt[]{3625} \\ h=5\sqrt[]{145}\approx60.2 \end{gathered}`

then, the rounded lenght of the diagonal is 60ft