Michael J. answered • 11/20/17

Effective High School STEM Tutor & CUNY Math Peer Leader

If you draw the rectangle with squares cut off at the corners, your resulting dimensions will be

length = 20 - 2x

width = 14 - 2x

height = x

These are the dimensions of the box. The height also represents the side length of the squares, since you fold the flat piece by the tabs to make the box. Multiply these them together to get your volume.

V = x(14 - 2x)(20 - 2x)

V = x(280 - 68x + 4x

^{2})Set V=270.

270 = 4x

^{3}- 68x^{2}+ 280xSubtract 270 on both sides of the equation.

0 = 4x

^{3}- 68x^{2}+ 280x - 270You now have a cubic equation. Use any method to solve for the zeros. Rational root theorem, synthetic division, or ever factor by grouping.