## 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.

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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.

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???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???

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