If I resize the width of an image in Keynote or Pages the height resizes as well. The same thing happens vice versa.
How can I resize the width without affecting the height and vice versa?
Select the picture, then in the Arrange tab uncheck Constrain Proportions [you may have to revert to original size before that will un-grey.
Then dragging the image by any edge will stretch.
If you need to crop, that's in Image - Edit Mask [though crop doesn't constrain anyway]