## Algebra: A Combined Approach (4th Edition)

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