The volume of a rectangular box with a square base is 175x^2+210x+63. If the height is 7 units, what is (show all work) a)the dimensions of the base b)the perimeter of the base
Thank you!
Since the base is square, then we can set $\displaystyle 7y^{2}=175x^{2}+210x+63$ and solve for y. Where y is the width(and length) of the base.
$\displaystyle \frac{175x^{2}+210x+63}{7}=25x^{2}+30x+9=(5x+3)^{2 }$
$\displaystyle y=\sqrt{(5x+3)^{2}}=|5x+3|$