# What is the length of a diagonal of a 15-mm-by-20-mm-by-8-mm rectangular prism?

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We know that the diagonal of a prism is given by :

D = sqrt(L^2 + w^2 + h^2) such that L, w, and h are the dimensions.

==> D = sqrt( 15^2 +20^2 + 8^2)

==> D = sqrt(225 + 400 + 64)

==> D = sqrt(689)

==> D = 26.25 mm.

**Then the diagonal of the prism is sqrt(689)=26.25 mm (approx.)**

The sides of the rectangular prism are 15 mm, 20 mm and 8 mm.

The length of the diagonal for a rectangular prism is given by

D = sqrt (w^2 + l^2 + h^2)

Substituting the values we have

D = sqrt (15^2 + 20^2 + 8^2)

=> sqrt( 689)

=> 26.24 ( approximately)

**The length of the diagonal of the prism is sqrt 689 mm.**