A rectangular box has a length of 12 inches and a width of 4 inches. The length of the three-dimensional diagonal of the box is 14 inches. What is the height of the box?
I would like to see how to get this answer so I would like a formula or a equation for me thanks!!
Since it is a three dimensional diagonal
Then It is a rectangular prism
Where
D²=l²+w²+h²
14²=12²+4²+h²
h²=14²-(12²+4²)
thanks y'all
To find the height of the box, we can use the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right-angled triangle equals the square of the length of the hypotenuse.
Let's label the length of the box as a, the width as b, and the height as h.
According to the given information:
a = 12 inches (length)
b = 4 inches (width)
c = 14 inches (length of the three-dimensional diagonal)
To find the height (h), we can set up an equation using the Pythagorean theorem:
a^2 + b^2 + h^2 = c^2
Substituting the given values:
(12^2) + (4^2) + h^2 = 14^2
Simplifying the equation:
144 + 16 + h^2 = 196
Combining like terms:
h^2 = 36
Taking the square root of both sides:
h = √36
Therefore, the height of the box is 6 inches.