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Let's just say I have a value like 46,080. I want to resize a rectangular image to have this area while maintaining its aspect ratio. What are some ways I can do that?

Here is an example.

Desired Area = 46,080

image width = 231
image height = 228
image area = 52,668

Decrease the dimensions of the image so it has an area of 46,080 while keeping its aspect ratio.

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2 Answers 2

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Let the desired area be $A$, and let the current dimensions be $x$ and $y$. Then, the current area is $xy$, so we must scale the area by a factor of $\displaystyle\frac{A}{xy}$.

Now, because are is proportional to the square of side length, side length is proportional to the square root of area, so we must scale $x$ and $y$ by $\displaystyle\sqrt{\frac{A}{xy}}$.

Thus, the new dimensions are $\displaystyle x\cdot \sqrt{\frac{A}{xy}}\text{ by }y\cdot\sqrt{\frac{A}{xy}}$, equivalent to $\boxed{\sqrt{\frac{Ax}{y}}\text{ by }\sqrt{\frac{Ay}{x}}.}$

For your case, just plug in $A = 46080, x = 231, y = 228$. You may want to round off the values you find.

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  • $\begingroup$ In your approach, does it matter if the image area was less than desired area? Because in my example, its not. $\endgroup$ Commented Jan 13, 2021 at 3:29
  • $\begingroup$ No, it does not matter. $\endgroup$ Commented Jan 13, 2021 at 4:24
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The aspect ratio $$\frac{231}{228}=1.013157895$$ The area ratio $$\frac{52668}{46080}=0.874914559$$ The area is gets a percentage from both sides so the contribution would be the square root of the area ratio. $$\sqrt{0.874914559}=0.935368676$$ $$231\times 0.935368676=216.070164\\ 228\times 0.935368676=213.264058$$

$$\frac{216.070164}{213.264058}=1.013157895$$

$$216.070164\times 213.264058$=46080$$

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