Question

HEIGHT OF A ROOM

Given the floor area of a room as 24 feet by 48 feet,and the space diagonal of the room as 58 feet,
can you find the height of the room?

Answer 1

let height of room = x feet
dimension of floor = 24 feet × 48 feet

space diagonal = 58 feet

$\sqrt{ x^{2} +24^2 + 48^2}=58\\ \\ \Rightarrow x^{2} +24^2 + 48^2=58^2\\ \\ \Rightarrow x^{2} +576 + 2304=3364\\ \\ \Rightarrow x^{2} =3364-576 - 2304=484\\ \\ \Rightarrow x= \sqrt{484}=22\ feet$

Height of room is 22 feet.