Question

A rectangular box has a length of 8 feet and a width of 2 feet. The length of the three-dimensional diagonal is 10 feet. What is the height of the box?

please answer

Answer 1

Answer:
`h=5.66ft`

Explanation:

Observe the picture attached.

Find the value of "x" and "y" using the Pythagoren Theorem:

`a^2=b^2+c^2`

If you solve for "a":

`a= √(b^2+c^2)`

Where "a" is the hypotenuse and "b" and "c" are the legs.

In this case, for "x" you know that:

`a=x\\b=8ft\\c=2ft`

Then, the value of "x" is:

`x=√((8ft)^2+(2ft)^2)\\\\x=8.24ft`

For "y" you can see that:

`a=10ft\\b=8.24ft\\c=h`

Subsituting values and solving for h, you get:

`(10ft)^2=(8.24ft)^2+h^2\\\\h=√((10ft)^2-(8.24ft)^2) \\\\h=5.66ft`