The trick is ensuring that the selected area you want meets the minimum size requirement you gave. That is, you’re not selecting a 50×80 area in the first place. If you do, then you’ll have to enlarge the result… and that just looks crappy.
So, for sanity’s sake, let’s assume your selected area is bigger than 100×130 pixels.
1. Make sure the Info palette is visible
2. Select the area you want ensuring the “W:” and “H:” attributes are >= the desired size. (If it’s already 100×130, well that’s a bonus!) Allow some space to exist around your perfect selection… might need it later.
3. Click the Image menu, and select Crop.
Now you need to shrink it down.
4. Click the Image menu, select Image Size…
5. Enter the value size you want in pixels. Ensure the “Constrain Proportions” checkbox is enabled.
And here’s where it gets a little tricky. You want to constrain the proportions so that the final image isn’t squished. But it’s likely that your selection isn’t proportional to the desired size.
So, plug in either Width or Height and, depending on which you tried, keep the value that allows your proportions to fit in. Like, if you plug in 100 for Width, then Height is auto-filled with another value, like 150, then that’s what you want to keep (150 > 130).
Here’s where the extra space from #2 comes into play.
6. You’ll want to recrop the image again. This time to get the perfect size, cropping off the extra Height (from my example in #4). Watch the Info palette to ensure you get the right dimensions.
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That’s a really simple and rough example. In reality, you’ll need to experiment a little bit on guessing at the proportions. So you might try it a couple of different ways, playing with selected area.
I’m also stuck in an older Photoshop… so if anyone can explain a new fangled approach, that’d probably be good for us all.