If you'd like to sew shorts with a close fit you can use the leggings pattern Lo! That pattern includes several variations, incl. to sew a cuffed or elasticated waist. The side seam is also marked in the pattern (however you'd need to add seam allowance to the side seam if you choose to make that, more info on this is included in the tutorial).
My oldest daughter wears size 110/116 right now, but I chose to sew size 122 (with an elasticated waist) for a more loose fit. (If you're sizing up like I did, don't forget that you don't have to make them as high in the waist).
From the front and back crotch I measured 8 cm (3.1") and along the side seam I measured 6 cm (2.4") from the height of the crotch and down. I then drew a curved line along these markings and here's where I cut the leggings to be shorts instead, and 2 cm (3/4") hem allowance is included.
These measurements are likely not the same for all sizes, but you could for example have a look in the child's wardobe and compare the length with another pair of shorts.
This is the result! As you can see I didn't sew a regular hem, but folded them instead. I first folded them 1 cm (3/8"), and then again 1 cm (3/8"), pressed and hand sewed at a couple of places to anchor the fold.
The beautiful fabric is "Hortensia pink", from WCollection Fabrics.