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? Show all of your work.
Im confused should i divide? or what should i do to find the answer? and what is the answer??
Please help! thanks!
12^2 + 4^2 + h^2 = 14^2
Did you make a sketch?
if you have a box with dimensions x by y by z
then the length of the diagonal is √(x^2 + y^2 + z^2) , that should be easy to see
so you have √(12^2 + 4^2 + h^2) = 14
square both sides:
144 + 16 + h^2 = 196
take over
To find the height of the box, we can use the Pythagorean Theorem in three dimensions. The Pythagorean Theorem states that in a right 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, the length, width, and height of the box form a right triangle. The length and width are two of the sides, and the height is the hypotenuse.
Let's label the sides of the triangle:
Length = 12 inches (side a)
Width = 4 inches (side b)
Height = ? (hypotenuse c)
Using the Pythagorean Theorem, we can write the equation:
a^2 + b^2 = c^2
Plugging in the values we know:
12^2 + 4^2 = c^2
144 + 16 = c^2
160 = c^2
To find the value of c (height), we need to find the square root of both sides of the equation:
√160 = √c^2
So, the height of the box is the square root of 160 inches, which simplifies to approximately 12.65 inches.