Answer
Length = 282.2 feet
Work Step by Step
The electrical resistance R of a wire varies directly with the length L of the wire and inversely with the square of the diameter D of the wire.
=> $R = k\frac{L}{D^2}$
L = 432 feet, D = 4mm gives R = 1.24 Ohms
=> $1.24 = k\frac{432}{4^2}$ =>$k =\frac{16*1.24}{432}$
To find L when R = 1.44 Ohms and D = 3mm
$1.44 = k\frac{L}{3^2}$ => $L =\frac{9*1.44}{k}$
=> $L =\frac{9*1.44}{\frac{16*1.24}{432}} = \frac{9*1.44*432}{16*1.24} = 282.2\ feet$
