Question

HELP


What is the longest line segment that can be drawn in a right rectangular prism that is 15cm long, 8 cm wide, and 7 cm talk

Answer 1

Answer:

=18.38cm

Step-by-step explanation:

The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment .

Look at the attached picture. The longest segment we can draw is AG (or any of its equivalent: BH, CE, DF). Let's focus on AG for example.

We can think of AG as the hypotenuse of triangle ACG. So, we need AC first. AC is itself the hypotenuse of triangle ABC,

so we have,

$AC^2 = AB^2+BC^2=8^2+7^2=113$

Now we can resume where we stopped with triangle AGC, and we have

$AG=\sqrt{AC^2+CG^2}=\sqrt{113+225}=\sqrt{338}$

=18.38cm