intermediate Geometry assist » hard Geometry » prisms » just how to uncover the diagonal line of a prism


You are watching: Find the length of the diagonal of the box

What is the length of the diagonal line of a rectangular box v the size of

*
?


*


*


*


*




See more: How To Get Rid Of A Voodoo Doll Curse, How Do You Get Rid Of A Cursed Voodoo Doll

Explanation:

To solve this problem we need an extension of the Pythagorean Theorem:

*

So the equation to resolve becomes

*

So the street of the diagonal is

*
.


Explanation:

The length of the diagonal line is indigenous the bottom left hand edge closest to us to the height right hand edge that"s farthest away indigenous us. 

This sort of a problem may it seems to be ~ to it is in a little more facility than it really is. 

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

For the an initial step of this problem, it"s valuable to imagine a triangle "slice" that"s gift taken inside the prism. 

*
, where the diagonal of attention is D2, and also D1 is the diagonal line that cut from edge to edge of the bottom confront of the prism. The this triangle that"s outlined in pink dashed lines, the offered information (the dimensions of the prism) provides a length for one of the legs (16). 

We can currently "map out" the D2 (the hypotenuse that the dashed triangle) deserve to be fixed by utilizing the Pythagorean to organize if us can achieve the length of the other leg (D1).

The next step the this trouble is to solve for D1. This will certainly be the an initial use that the Pythagorean theorem. D1 is the diagonal of the base and is limited to a 2D face. This can be represented as:

*

The hypotenuse the the base, or the mystery length leg of the dashed triangle, can be solved by utilizing the Pythagorean Theorem:

*

*

*

*

*

*

*

Now that we calculated the size of D1, D2 have the right to be solved for by using the Pythagorean to organize a second time: