## Formula for the diagonal line in regards to the length, width, and also height the the rectangle-shaped prism

The diagonal line of a right rectangle-shaped prism goes native one corner of the prism, throughout the interior volume, every the method to the opposite corner of the prism.

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

You can uncover the length of a diagonal of a right rectangular prism using

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

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

## Length of the diagonal of a right rectangular prism

**Example**

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

Not all of the dimensions here are the same. Change ???60 ext mm??? come centimeters first.

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

Then the dimensions are

Plugging these right 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 of a right rectangle-shaped prism goes indigenous one edge of the prism, throughout the internal volume, every the way to the opposite edge of the prism.

We just need come plug the size we’ve been given into the formula for the diagonal.

See more: What Are The Processes By Which Moisture Is Added To Unsaturated Air? ?

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

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

Manipulate the equation to settle 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, learn online, virtual course, virtual math, geometry, three-dimensional geometry, 3D geometry, prisms, rectangular prisms, right rectangle-shaped prisms, diagonal of the prism, diagonal of the rectangular prism, diagonal line of the right rectangle-shaped prism, diagonal line

learn mathKrista KingAugust 30, 2020math, learn online, virtual course, online math, stats, statistics, probability and also stats, probability and also statistics, studies, varieties of studies, sampling, observational studies, speculative studies, suitable pairs, matched pairs experiments

learn mathKrista KingAugust 30, 2020math, find out online, virtual course, virtual math, algebra, algebra 1, algebra i, equation the a line, slope-intercept form, slope, steep of a line, y=mx+b