High School Why Does Poisson's Ratio Show Equal Transverse Strain in 3D Rectangles?

[Kabo111]

In poisson's ratio

If we are stretching a a 3d rectangle
L is height
A,B are the length and width
Starching it in the L direction so that's the longitudinal strain we are making
Why does the transverse strain in the "a " side equals the strain in "b" side
So like that we can both use ∆a/a or ∆b/b
To get the transverse strain ?
I mean why is ∆a/a=∆b/b ..
Please in a simple way first , sorry for bad English or typos, I'm using my phone to submit this. Thx all.

 

[Chestermiller]

The bar of rectangular cross section is in a state of homogeneous stress. What is the stress in the “a” direction? What is the stress in the “b” direction?