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What is the length, in units, of the shortest possible diagonal of a rectangle with all integer side lengths and perimeter 26 units?Express your answer in simplest radical form.

 Mar 20, 2018
 #1
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If the perimeter is 26....the length and width sum  is  1/2 of this  =  13

 

So.....using the Pythagorean Theorem

L    W

12  1   produces a diagonal of √ [12^2 + 1^2]   = √145

11  2      = √[11^2 + 2^2 ]  =  √125

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.

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7   6       ≈ √ [ 7^2 + 6^2 ]  = √85

 

And this is the shortest diagonal possible for the given conditions

 

 

cool cool cool

 Mar 20, 2018

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