## 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.

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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.

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???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???

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