#### Answer

The lengths of the sides are $13, 8, 10, 16$

#### Work Step by Step

lets calculate the perimeter using x.
$Perimeter = (2x + 3) + (x+3)+(3x+1)+(x^2-3x) = 2x+3+x+3+3x+1+x^2-3x = x^2 + 3x + 7$
We know that the Perimeter equal to 47.
Therefore
$x^2 + 3x + 7 = 47$
$x^2 + 3x + 7 - 47 = 47 -47$
$x^2 + 3x -40 = 0$
$x^2 - 5x + 8x -40 = 0$
$x ( x-5) + 8 ( x-5) = 0$
$(x+8 )(x-5) = 0$
x equal -8 or 5.
it cannot be -8 because then we will have a negative length of the sides.
Therefore $x = 5$
The lengths of the sides are $13, 8, 10, 16$