Formula because that the diagonal in terms of the length, width, and also height the the rectangle-shaped prism

The diagonal of a right rectangular prism goes native one edge of the prism, throughout the interior volume, all the means to the opposite edge of the prism.

You are watching: Length of diagonal of a box


*

*

You can discover the size of a diagonal of a right rectangle-shaped prism using

???d=sqrtl^2+w^2+h^2???

where ???d??? is the length of the diagonal, and ???l???, ???w???, and also ???h??? room the length, width, and height, respectively.



*

Length the the diagonal line of a right rectangle-shaped prism

Example

What is the size of the diagonal line of the right rectangle-shaped prism?


*

Not every one of the dimensions right here are the same. Adjust ???60 ext mm??? come centimeters first.

???60 ext mm=6 ext cm???

Then the dimensions are


Plugging these into the formula because that the diagonal, we get

???d=sqrtl^2+w^2+h^2???

???d=sqrt7^2+12^2+6^2???

???d=sqrt49+144+36???

???d=sqrt229??? cm


The diagonal line of a right rectangle-shaped prism goes native one edge of the prism, across the inner volume, every the means to the opposite edge of the prism.


We simply need come plug the size we’ve been provided into the formula for the diagonal.

See more: Exercise May Transform The Chemical Energy In The Food You Eat Into ?

???d=sqrtl^2+w^2+h^2???

???7sqrt2=sqrt5^2+w^2+3^2???

Manipulate the equation to solve for ???w???.

???(49)(2)=5^2+w^2+3^2???

???98=25+w^2+9???

???98=34+w^2???

???64=w^2???

???8=w???


discover mathKrista KingAugust 30, 2020math, discover online, virtual course, virtual math, geometry, three-dimensional geometry, 3D geometry, prisms, rectangle-shaped prisms, right rectangular prisms, diagonal of the prism, diagonal of the rectangular prism, diagonal line of the right rectangular prism, diagonal line
discover mathKrista KingAugust 30, 2020math, learn online, virtual course, digital math, stats, statistics, probability and also stats, probability and also statistics, studies, varieties of studies, sampling, observational studies, speculative studies, matched pairs, matched pairs experiments
learn mathKrista KingAugust 30, 2020math, find out online, digital course, digital math, algebra, algebra 1, algebra i, equation the a line, slope-intercept form, slope, slope of a line, y=mx+b