# Get Scaling Factor from a Rectangle

Let say I have a rectangle with width and height in meters. Now, I need to scale down my rectangle with x meters. How can I find scaling factor?

-

## 1 Answer

The scaling factor that shortens the height $h$ by $x$ meters is $\lambda = \frac{h-x}{h}$. The same applies to the widdth $w$. Of course, unless $w=h$ there is no scaling factor that shortens both $w$ and $h$ by $x$ meters.

If you want to rescale $w$ and $h$ such that the area is $x$ square meters less, then any two numbers $\eta$ (scale factor for height) and $\xi$ (scale factor for width) such that $\eta\cdot \xi = \frac{h\cdot w - x}{h \cdot w}$ will do.

-
Thanks. This is very nice explaination. It's mean η⋅ξ is the scaling factor for me. –  user960567 Mar 29 '12 at 10:23
you are welcome. –  fabee Mar 29 '12 at 14:40
Do you know the answer of this question? math.stackexchange.com/questions/126151/… –  user960567 Mar 30 '12 at 3:54