Answer
The newly measured length will be about 0.25 meters
Work Step by Step
We were given the velocity and asked for the new measured length. We can see from the graph given that $L_0=0.80m$.
We can now use the length contraction equation to solve for the measured length;
$L=L_0 \sqrt{1-\beta^2}$
$L=0.80m \sqrt{1-(0.95)^2}$
$L=0.25m$