Question

in the rectangular prism below, the length of \\( \overline{mr} \\) is 8 inches, the length of \\( \overline{rs} \\) is 9 inches, and the length of \\( \overline{st} \\) is 12 inches.

what is the length of a line segment drawn from point t to point m?

a. 17 inches
b. 15 inches
c. 21 inches
d. 29 inches

Explanation:

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

The formula for the space - diagonal \(d\) of a rectangular prism with length \(l\), width \(w\), and height \(h\) is \(d=\sqrt{l^{2}+w^{2}+h^{2}}\). Here, \(l = 12\) (length of \(\overline{ST}\)), \(w = 9\) (length of \(\overline{RS}\)), and \(h = 8\) (length of \(\overline{MR}\)).

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Answer:

A. 17 inches