Answer
10 inches
7 inches
7 inches
5 inches
Work Step by Step
Let the sides of the quadrilateral are $x,y,z$ and $w$.
Given,
longest side $x $ is twice the shortest side $w$
$x= 2w$
Other two sides are equal.
$y=z$
$y $ is $2$ inches longer than the shortest side $w$
$y=2+w$
Perimeter of the quadrilateral is $29$ inches.
$x+y+z+w=29$
$2w+2+w+2+w+w=29$
$5w+4=29$
$5w=25$
$w=5$
Lengths of all four sides
$x=2 \times 5 =10$ inches
$y= 2 + 5 = 7$ inches
$z=7 $ inches
$w= 5$ inches