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When a square with area 9 is dilated by a scale factor of k we obtain a square with area 25 Find the sum of all possible values of k

 Nov 11, 2023
 #1
avatar+10 
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The side lengths of the original square and the new square are 3 and 5. Therefore, there are two values of k: 5/3 and -5/3. Note: you can dilate by a negative scale factor, think about the square on a cartesian plane. Therefore sum of the values of k are 0.

 Nov 11, 2023
 #2
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Another solution for this problem is using algebra.

Erwus's solution was probably cleaner, but I might as well post mine.

 

Let n be the side length of the square

n^2 = 9

(kn)^2 = 25

k^2*n^2 = 25

k^2 * 9 = 25

k^2 = 25/9

k = √25/9

= 5/3 or - 5/3

So 5/3 +(-5/3) = 0

Darkness  Nov 13, 2023

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