intermediary Geometry aid » heavy Geometry » prisms » exactly how to uncover the diagonal of a prism


You are watching: Length of a diagonal of a box

What is the size of the diagonal line of a rectangular box with the size of

*
?


*


*


*


*




See more: Anytime At Your Convenience In A Sentence Examples, How To Use At Your Convenience In A Sentence

Explanation:

To deal with this trouble we need an expansion of the Pythagorean Theorem:

*

So the equation to settle becomes

*

So the street of the diagonal is

*
.


Explanation:

The size of the diagonal is native the bottom left hand corner closest to us to the peak right hand corner that"s farthest away from us. 

This type of a difficulty may it seems ~ to it is in a little more complex than it really is. 

In order to fix for the diagonal length, every that"s required is the Pythagorean Theorem. This equation will certainly be used twice to solve for the dashed line. 

For the first step that this problem, it"s beneficial to imagine a triangle "slice" that"s being taken within the prism. 

*
, where the diagonal of attention is D2, and D1 is the diagonal line that cut from edge to edge of the bottom face of the prism. That this triangle that"s outlined in pink dashed lines, the given information (the dimensions of the prism) offers a length for one of the foot (16). 

We can currently "map out" the D2 (the hypotenuse of the dashed triangle) have the right to be resolved by using the Pythagorean organize if us can acquire the length of the various other leg (D1).

The next step of this trouble is to fix for D1. This will certainly be the very first use that the Pythagorean theorem. D1 is the diagonal line of the base and is minimal to a 2D face. This have the right to be stood for as:

*

The hypotenuse the the base, or the secret length leg of the dashed triangle, deserve to be fixed by using the Pythagorean Theorem:

*

*

*

*

*

*

*

Now that we calculated the length of D1, D2 have the right to be resolved for by utilizing the Pythagorean organize a second time: