Question

A packaging company is planning is in the planning stages of creating a box that include a three dimensional support inside the box.The box has a width of 5 feet a length of 6 feet and a height of 8 feet. How long will the diagonal support need to be

Answer 1

The length of the diagonal support is 69 feet.

Explanation:

Dimensions of the box: length = 6 feet

width = 5 feet

height = 8 feet

The diagonal support relates with the diagonal of the base and the height.

From the base of the box, let the length of its diagonal be represented by x. Applying Pythagoras theorem;

`/Hyp/^(2)` =
`/Adj 1/^(2)` +
`/Adj 2/^(2)`

`x^(2)` =
`6^(2)` +
`5^(2)`

`x^(2)` = 36 + 25

= 61

x =
`√(61)`

= 7.81

let the length of the diagonal support be represented by l. So that;

`/Hyp/^(2)` =
`/Adj 1/^(2)` +
`/Adj 2/^(2)`

`l^(2)` =
`x^(2)` +
`8^(2)`

=
`√(61)` + 64

l =
`\sqrt{√(61) + 64 }`

= 61 + 8

= 69

Thus, the length of the diagonal support is 69 feet.