Answer
$16$ in. by $16$ in.
Work Step by Step
Given,
Length of the box $(l) = (x-6)$ in.
Width of the box $(w) =(x-6)$ in.
Height of the box $ (h) =3$ in.
Volume $(V) = 300$ cubic inches.
Volume of the box $V = l \times w \times h$
$300 = (x-6) \times (x-6 ) \times 3$
$ (x-6)^{2} = 100 $
Using $(a-b)^{2} = a^{2} -2ab +b^{2} $
$ x^{2} -12x +36 =100 $
$ x^{2} -12x +36-100 = 0$
$ x^{2} -12x - 64 = 0$
By factoring,
$(x-16)(x+4)=0$
$x=16$ or $x=-4$
Length (and the width ) should not be negative.
So, the dimensions of the square cardboard is $16$ in. by $16$ in.
Check:
Volume of the box
$V = l \times w \times h$
$V = (x-6) \times (x-6 ) \times 3$
Substituting $x=16$
$V = (16-6) \times (16-6 ) \times 3$
$V = 10 \times 10 \times 3$
$V = 300$ cubic inches.
