At what speed v will the length of a 1.00 m stick look 13.7 % shorter (86.3 cm )
using formula l=lp sqrt 1-v^2/c^2

L= Lp - 13.7*Lp/100 = Lp-0,137Lp = 0,8613Lp

⇒L/Lp = 0.8613

From the formula above L/Lp = √(1-v^2/c^2)

(L/Lp)^2 = 1 - (v^2/c^2)

v^2/c^2 = 1 - (L/Lp)^2

v/c = √[1 - (L/Lp)^2]

v = c √[1-(L/Lp)^2]

v =c√[1-0.8613^2] = 0.508c

In the vacumm speed of light, c,  is approx 300,000,000 m/s

v =0.508 (300,000,000m/s) =152,400,000 m/s

Please, let me know if this helped you.