  Finding a suitably growing length scale that increases in tandem with the
immense viscous slowdown of supercooled liquids is an open problem associated
with the glass transition. Here, we define and demonstrate the existence of one
such length scale which may be experimentally verifiable. This is the length
scale over which external shear perturbations appreciably penetrate into a
liquid as the glass transition is approached. We provide simulation based
evidence of its existence, and its growth by at least an order of magnitude, by
using molecular dynamics simulations of NiZr2, a good fragile glass former. On
the probed timescale, upon approaching the glass transition temperature from
above, this length scale, {\xi} is also shown to be consistent with Ising-like
scaling. Furthermore, we demonstrate the possible scaling of {\xi} about the
temperature at which super-Arrhenius growth of viscosity, and a marked growth
of the penetration depth sets in. Our simulation results suggest that upon
supercooling, marked initial increase of the shear penetration depth in fluids
may occur in tandem with the breakdown of the Stokes-Einstein relation.
