Answer
width = 5 cm, length = 6 cm
Work Step by Step
width is 7 less than 2* length
$w = -7+2*l$
$a = l*w$
$A = l*(2l-7)$
$A = 2l^2-7l$
$30 =2l^2-7l$
$2l^2-7l-30=0$
$2x^2-7x-30$
$2x^2+5x-12x-30$
$x(2x+5)-6(2x+5)$
$(2x+5)(x-6)$
$2l^2-7l-30=0$
$(2l+5)(l-6)=0$
$2l+5=0$
$2l=-5$
$2l/2=-5/2$
$l=-2.5$ (not a valid solution since we can't have a negative length)
$l-6=0$
$l=6$
$w = -7+2*l$
$w = -7+2*6$
$w = -7+12$
$w=5$
