Question

in the rectangular prism below, ( jn = 29 ), ( jk = 20 ), and ( jl = 28 ). find the length of the diagonal ( overline{jm} ). if applicable, round your answer to the nearest whole number. the lengths on the figure are not drawn accurately.

Explanation:

Step1: Apply the formula for the space - diagonal of a rectangular prism

The formula for the space - diagonal \(d\) of a rectangular prism is \(d=\sqrt{l^{2}+w^{2}+h^{2}}\). In a rectangular prism, if we consider the right - triangle relationships, we can also use the fact that if \(JN\) is the diagonal of the base (or a face) and \(JL\) is another edge, and we want to find the space - diagonal \(JM\). By the Pythagorean theorem in three dimensions, \(JM^{2}=JN^{2}+JL^{2}\) (since in a rectangular prism, the edges are perpendicular to each other).
Given \(JN = 29\) and \(JL=28\).

Step2: Calculate \(JM\)

Substitute the values into the formula \(JM=\sqrt{JN^{2}+JL^{2}}\).

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Answer:

\(40\)