Square A Pallet

[Friendly]

Hello,
Sometimes I build very large wood pallets at work, and I square them by measuring diagonally corner to corner. This isn't difficult to do, but I am lazy, and I want to be able to figure the distance by the length and width, since I already have these dimensions.

 

[mmm4444bot]

Hello Friendly Pallet Builder:

It sounds to me like you need the Pythagorean Theorem.

If the length and width of a rectangle have the same measure, then the rectangle is a square. In this case, the Pythagorean Theorem simplifies, and the length of the diagonal is:

side length * sqrt(2)

(The asterisk is a multiplication symbol, and sqrt(2) means the square root of 2.)

For example, if a square measures 9 feet by 9 feet, then its diagonal measures 9 * sqrt(2) feet.

The square root of 2 is about 1.4142.

side length * sqrt(2) = 9 * sqrt(2) = 9 * 1.4142 = 12.7279

The diagonal of a 9 x 9 square is about 12.73 feet.

Does this help ?

I'm not sure if "squaring them" means making pallets that are squares. If you have some specific measurements for rectangles that are not squares, I will show you how to use the Pythagorean Theorem to find their diagonals:

diagonal = sqrt(length^2 + width^2)

Cheers,

~ Mark

 

[Friendly]

I appreciate your response. I will study this, and of course I will be using my calculator to cheat.

I guess I'm using square in a generic sense. By square I mean they measure the same diagonally both ways. Most of the time the pallets are rectangles, not squares.

 

[Friendly]

You explain things very well. Could you tell please tell me what the top hat operator (^) means? I have forgotten.

 

[mmm4444bot]

The caret symbol (^) is used to show exponentiation.

9^2 means 9[sup:36n0jx32]2[/sup:36n0jx32] (read as "nine squared")

These are abbreviations for repeated multiplication.

In other words, the exponent 2 tells us how many factors of the base 9 are multiplied together.

Examples:

9^2 = 9 * 9 = 81

9^3 = 9 * 9 * 9 = 729 (read as "nine cubed")

9^4 = 9 * 9 * 9 * 9 = 6561 (read as "nine to the fourth")

5^3 = 5 * 5 * 5 = 125 ("five cubed")

2^4 = 2 * 2 * 2 * 2 = 16 ("two to the fourth")

--------------------------------------------------------

Examples of finding diagonal of rectangles:


4 foot by 7 foot rectangle

diagonal = sqrt(4^2 + 7^2)

= sqrt(4*4 + 7*7)

= sqrt(16 + 49)

= sqrt(65), which is about 8.06 feet



11 foot by 5 foot rectangle

diagonal = sqrt(11^2 + 5^2)

= sqrt(11*11 + 5*5)

= sqrt(121 + 25)

= sqrt(145), which is about 12.08 feet



7.75 foot by 14.25 foot rectangle

diagonal = sqrt(7.75^2 + 14.25^2)

= sqrt(60.0625 + 203.0625)

= sqrt(263.1250), which is about 16.22 feet



Are you good to go ?



PS: It's not really cheating to use a calculator for this stuff; hardly anybody calculates square roots by hand anymore.

 

[Friendly]

Yes! Thanx for your help!