Geometry problem (Pepperoni Truck Problem)

[rfxw]

I have this math problem:

The Lucaso Specialty Meats Company produces a cocktail pepperoni unlike no other. Before they are cut into shorter lengths for packaging they are very long and very stiff- can't bend them- and very thin. Lucaso has a few customers who want their pepperonis uncut- they want the longest possible pepperoni they can get. Lucaso transport the pepperoni in refrigerated trucks. There is only one door. When the doors are open the opening is a rectangle in the exact center of the side of the truck's "box" that is four feet long and four feet high. The inside dimensions of the "box" are 40ft long, 7 ft wide and 8 ft high. What is the longest pepperoni stick that can be carried in this truck?... Round your answer down to the nearest inch. :?

 

[soroban]

Hello, rfxw!

The Lucaso Specialty Meats Company produces a cocktail pepperoni unlike no other.
Before they are cut into shorter lengths for packaging they are very long and very stiff
- can't bend them - and very thin.
Lucaso has a few customers who want their pepperonis uncut
- they want the longest possible pepperoni they can get.

Lucaso transports the pepperoni in refrigerated trucks; there is only one door.
When the doors are open the, opening is a four-foot square
in the exact center of the side of the truck's "box".
The inside dimensions of the "box" are 40ft long, 7 ft wide and 8 ft high.

What is the longest pepperoni stick that can be carried in this truck?
Round your answer down to the nearest inch.

If I interpret the problem correctly, the diagram looks like this:

              : - - - - - - - 40  - - - - - - - - :
              *-----------------------------------*Q
            /                                   / |
          /                                   /   |
        /                                   /     |
      *-----------------------------------*       |8
      |                                   |       |
      |                                   |       |
      |                 4                 |       |
     8|             *-------*             |       *
      |             |       |             |     /
      |            4|       |             |   / 7
      |             |       |             | /
      *-------------*-------*-------------*
      :     18      P        22           :

THe longest pepperoni that will fit into the truck will extend
from P (lower-left corner of the door) to Q (upper-right corner of the opposite wall).

This is the diagonal of a "box" which is 22 feet by 7 feet by 8 feet.
. . . . . . . . . . . . . . . . ___________ . . . . ___
The length is: .d .= .√22² + 7² + 8² .= .√597 .= .24.43358345 feet.

Therefore, the maximum length is: 24 feet, 5 inches.

 

[rfxw]

You are the man! Thank you!

You are the man, Soroban!!

 

[Denis]

Therefore, the maximum length is: 24 feet, 5 inches.

Sure will look funny walking the sidewalk while chewing on one of those :lol:

 

[Denis]

Re: You are the man! Thank you!

You are the man, Soroban!

After Soroban retired, he got a part time job delivering pepperoni sticks;
that's how he knows :idea: