Height of the room

Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room?

Result

c =  16 ft

Solution:

a=24 ft b=48 ft d=56 ft  d2=a2+b2+c2  c=d2a2b2=562242482=16 fta=24 \ \text{ft} \ \\ b=48 \ \text{ft} \ \\ d=56 \ \text{ft} \ \\ \ \\ d^2=a^2+b^2+c^2 \ \\ \ \\ c=\sqrt{ d^2-a^2-b^2 }=\sqrt{ 56^2-24^2-48^2 }=16 \ \text{ft}



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