SOLUTION: The perimeter of a 2 by 4 board cross-section is 10.5 in. Length is twice width. Determine dimensions of cross-section. Perimeter = 2L + 2W Length = 2W A 2 by 4 is 2 in.

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Question 1164005: The perimeter of a 2 by 4 board cross-section is 10.5 in. Length is twice width. Determine dimensions of cross-section.
Perimeter = 2L + 2W
Length = 2W
A 2 by 4 is 2 in. thick(or high) and 4 in. wide.
Not sure how to proceed.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52756)   (Show Source): You can put this solution on YOUR website!
.

Perimeter = 2L + 2W

Length L = 2W.


So, replace L by 2W in the first equation, based on the second relation.  You will get

    2*(2W) + 2W = 10.5

    4W     + 2W = 10.5 

    6W          = 10.5

     W          = 10.5/6 = 1.75.


Thus the width of the cross-section is 1.75 in.


Then the length of the cross section is  2*1.75 = 3.5 in.

Solved.



Answer by greenestamps(13195)   (Show Source): You can put this solution on YOUR website!


Note that, in real life, a (finished) 2x4 board is 3.5 inches wide and 1.75 inches thick, as the solution from the other tutor shows.

I think there are "raw" 2x4 boards that are in fact 4 inches wide and 2 inches thick....
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