Answer
13 cm, 15 cm, 22 cm, 70 cm
Work Step by Step
perimeter is sum of all side lengths
$(x+5)+(x+3)+(x^2-3x)+(3x-8)=120$
$x+5+x+3+x^2-3x+3x-8=120$
$2x+8+x^2-8=120$
$2x+x^2=120$
$x^2+2x-120=0$
$x^2+2x-120$
$x^2+12x-10x-120$
$x(x+12)-10(x+12)$
$(x-10)(x+12)=0$
$x-10=0$
$x=10$
$x+12=0$
$x=-12$ (we can't have a negative length, so this answer is invalid)
$x+5$
$10+5$
$15$
$x+3$
$10+3$
$13$
$x^2-3x$
$10^2-3*10$
$100-30$
$70$
$3x-8$
$3*10-8$
$30-8$
$22$
$15+13+70+22$
$28+92$
$120$
