The floor area of the room as 24 feet by 48 feet ,the space diagonal of the room as 56 feet. Find height
24^2 + 48^2 + h^2 = 56^2
To find the height of the room, we can use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, we can consider the length, width, and height of the room as the three sides of a right-angled triangle.
Let's assume that the length of the room is the base, the width of the room is the height, and the space diagonal is the hypotenuse.
Using the Pythagorean Theorem:
Length^2 + Width^2 = Hypotenuse^2
24^2 + 48^2 = 56^2
576 + 2304 = 3136
2880 = 3136
Now, let's solve for the height (width of the room):
2880 = 3136 - Width^2
Width^2 = 3136 - 2880
Width^2 = 256
Taking the square root of both sides:
Width = √256
Width = 16 feet
Therefore, the height (width of the room) is 16 feet.
To find the height of the room, we can use the Pythagorean theorem.
Let's denote the length of the room as L, the width of the room as W, and the height of the room as H.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the space diagonal of the room can be considered as the hypotenuse of a right-angled triangle.
So, we have:
(L^2 + W^2) = (space diagonal^2)
Plugging in the values, we get:
(24^2 + 48^2) = 56^2
Simplifying further:
(576 + 2304) = 3136
2880 = 3136
To find the height, we need to solve for H in the equation:
(H^2 = space diagonal^2 - L^2 - W^2)
Plugging in the values, we get:
(H^2 = 56^2 - 24^2 - 48^2)
(H^2 = 3136 - 576 - 2304)
(H^2 = 3136 - 2880)
(H^2 = 256)
Taking the square root of both sides:
H = √256
H = 16
Therefore, the height of the room is 16 feet.