# 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?

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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.