The longest line segment that can be drawn in a right rectangular prism that is 14cm long, 13cm wide and 11cm tall is 19.1cm.
What is a right rectangular prism?
A right rectangular prism is a three dimensional solid shape formed by 6 rectangles.
it is also called the cuboid.
Analysis:
The diagonal of the face of the prism with dimensions 14cm long and 13cm wide is the longest line segment that can be drawn.
Since rectangles have 90° on each vertex, we can use Pythagoras theorem to calculate for the length of the diagonal.
[tex](diagonal)^{2}[/tex] = [tex](length)^{2}[/tex] + [tex](width)^{2}[/tex]
[tex](diagonal)^{2}[/tex] = [tex](14)^{2}[/tex] + [tex](13)^{2}[/tex]
= 196 + 169 = 365
[tex](diagonal)^{2}[/tex] = 365
diagonal = [tex]\sqrt{365}[/tex] = 19.1cm
In conclusion, the length of the longest diameter is 19.1cm
Learn more about Right rectangular prism: brainly.com/question/3317747
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