A rectangular box has a length of 12 inches and a width 4 inches. The length of the three-dimensional diagonal of the box is 14 inches. What is the height of the box?
let the height be h
h^2 + 12^2 + 4^2 = 14^2
h^2 + 144 + 16 = 196
h^2= 36
h = √36 = 6
To find the height of the box, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the length and width of the box form the base of a right triangle, and the height of the box is the third side (the hypotenuse) of the triangle. Let's call the height of the box "h".
Using the Pythagorean theorem, we can set up the equation:
(Length)^2 + (Width)^2 = (Height)^2
Substituting the given values into the equation, we have:
12^2 + 4^2 = h^2
Simplifying, we get:
144 + 16 = h^2
160 = h^2
Taking the square root of both sides, we get:
√160 = h
Approximately, h ≈ 12.65 inches
Therefore, the height of the box is approximately 12.65 inches.
To find the height of the box, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the hypotenuse represents the three-dimensional diagonal of the box, the length of the box represents one of the sides, and the width represents another side.
Let's label the height of the box as "h".
According to the given information, the length of the box is 12 inches, the width is 4 inches, and the three-dimensional diagonal is 14 inches.
Using the Pythagorean theorem, we can write the following equation:
h^2 + 4^2 + 12^2 = 14^2
Simplifying the equation:
h^2 + 16 + 144 = 196
h^2 + 160 = 196
Subtracting 160 from both sides:
h^2 = 36
Taking the square root of both sides:
h = √36
Simplifying:
h = 6
Therefore, the height of the box is 6 inches.