In the rectangular prism below, the length of MR is 8 inches, the length of RS is 9 inches, and the length of ST is 12 inches.
What is the length of a line segment drawn from point T to point M?

Step-by-step explanation:

if these are the lenghs you meant the we use this formula

12^2+8^2=c^2

144+64=208

c=14.22

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.