Question

What is the longest line segment that can be drawn in a right rectangular prism that is 14cm​ long, 13cm​ wide, and 11cm​ tall?

Answer 1

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.

$(diagonal)^{2}$ = $(length)^{2}$ + $(width)^{2}$

$(diagonal)^{2}$ = $(14)^{2}$ + $(13)^{2}$

                 = 196 + 169 = 365

 $(diagonal)^{2}$ = 365

diagonal = $\sqrt{365}$ = 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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