SOLUTION: Amy has a pen 13 cm long that she wants to send as a gift to a friend. She finds a rectangular box in which the pen just fits. The length and width of the box are 3 cm and 12 cm re

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Question 1208866: Amy has a pen 13 cm long that she wants to send as a gift to a friend. She finds a rectangular box in which the pen just fits. The length and width of the box are 3 cm and 12 cm respectively. What is the height of the box?
Found 2 solutions by timofer, ikleyn:
Answer by timofer(104) About Me  (Show Source):
You can put this solution on YOUR website!
Pythagorean Theorem, in three dimensions.
The pen extends between two opposite corners. You already have values for two of them and you
want to solve for the unknown dimension's value.

d%5E2%2B2%5E2%2B12%5E2=13%5E2
d%5E2=169-4-144
d%5E2=169-148
d=sqrt%2811%29
d=3.32

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
Amy has a pen 13 cm long that she wants to send as a gift to a friend. She finds a rectangular box
in which the pen just fits. The length and width of the box are 3 cm and 12 cm respectively.
What is the height of the box?
~~~~~~~~~~~~~~~~~


I came to fix the errors in the solution by the other tutor.


Pythagorean Theorem, in three dimensions.
The pen extends between two opposite corners. You already have values for two of them and you
want to solve for the unknown dimension's value. 

d%5E2%2B3%5E2%2B12%5E2 = 13%5E2

d%5E2 = 169-9-144

d = sqrt%2816%29

d = 4 cm.     ANSWER

Solved (correctly).