Andrew M. answered • 02/20/18

Tutor

New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

length: x cm

width: x - 12 cm

height: 5 cm

Volume = L*W*H = 5x(x-12) = (5x

^{2}- 60x) cm^{3}The box can hold "AT MOST" 1900 cm meaning it can hold from 0 to 1900 cm

^{3}giving us:**5x**-

^{2}**60x ≤ 1900**

Factoring out a 5 this can be written as:

**x**^{2}- 12x ≤ 380Working this as a quadratic to find the maximum dimensions:

x

^{2}- 12x - 380 = 0x = [12 ±√((-12)

^{2}-4(1)(-380))]/2x = (12±√1664)/2

x = (12 ±40.792)/2

x = 6 ± 20.396

Discarding the negative:

x =

**26.396 cm length**x-12 =

**14.396 cm width****height = 5 cm**

volume: LWH = 26.396(14.396)(5) = 1899.98 ≅ 1900 cm

^{3}The small discrepancy is due to rounding errors

Michael P.

02/20/18