AI Tutor
When you resize a photo by dragging only the right edge of the frame, the picture stretches horizontally while its height stays completely frozen.
This is non-proportional scalingβ€”changing an object's dimensions along different axes by different scale factors.
If uniform scaling multiplies area by k2k^2, how does area behave when each direction has its own separate multiplier?

Independent Scaling on Rectangles

A scale factor is a multiplier applied to a linear measurement. Let a horizontal scale factor be sxs_x and a vertical scale factor be sys_y.
For a rectangle with original width ww and height hh, the new dimensions are wβ€²=sxww' = s_x w and hβ€²=syhh' = s_y h.
Because area is length times width, the new area becomes Aβ€²=(sxw)(syh)=(sxsy)(wh)=(sxsy)AA' = (s_x w)(s_y h) = (s_x s_y)(wh) = (s_x s_y) A. The area scales by the product of both scale factors.
What happens to the perimeter under this same transformation?

The Perimeter Transformation

The original perimeter is P=2w+2hP = 2w + 2h. After scaling, the new perimeter is Pβ€²=2(sxw)+2(syh)=2sxw+2syhP' = 2(s_x w) + 2(s_y h) = 2s_x w + 2s_y h.
Unlike area, you cannot factor out a single combined multiplier for perimeter unless sx=sys_x = s_y. The new perimeter depends directly on the original individual side lengths.