The diagonal of the rectangular solid is [tex]d=2 \sqrt{21}[/tex]
Explanation:
The length of the rectangular solid is [tex]l=8[/tex]
The width of the rectangular solid is [tex]w=4[/tex]
The height of the rectangular solid is [tex]h=2[/tex]
We need to determine the diagonal of the rectangular solid.
The diagonal of the rectangular solid can be determined using the formula,
[tex]d=\sqrt{l^{2}+w^{2}+h^{2}}[/tex]
Substituting the values [tex]l=8[/tex], [tex]w=4[/tex] and [tex]h=2[/tex] , we get,
[tex]d=\sqrt{8^{2}+4^{2}+2^{2}}[/tex]
Squaring the terms, we get,
[tex]d=\sqrt{64+16+4}[/tex]
Adding the terms, we have,
[tex]d=\sqrt{84}[/tex]
Simplifying, we have,
[tex]d=2 \sqrt{21}[/tex]
Thus, the diagonal of the rectangular solid is [tex]d=2 \sqrt{21}[/tex]
