Please help me to find the length of the dashed line in this problem...

Question

 

In the problem it shows a box with a height of 8 cm, a length of 9cm, and a width of 12 cm. Running through the middle of the inside of the box is a dashed line. What is the length of the dashed line? 

Answer 1

I'm assuming the line runs from opposite corners of the box. 

 

Now, there is a right triangle formed:

Leg One: the edge of the box of height 8.

Leg Two: diagonal running the base of the box.

The Hypotenuse of this right triangle is the dotted line.

 

Leg Two is the diagonal through the box of dimensions 9x12.  It's length is  √(9² + 12²) = 15

 

The dotted line is of length √(15²+8²) = √269 = 17

Answer 2

By chance, are you referring to the length of the longest diagonal of the box?

 

If so, (length of diagonal)²=sum of squares of lengths of each dimension