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