A box in the shape of a rectangular prism has a volume of 2500cm^3.

Question

FULL QUESTION A box in the shape of a rectangular prism has a volume of 2500cm^3. The box is 4 times as wide as it is deep and 5 cm longer than it is wide.Dimensions of the box?we are doing polynomial equations,

we need to use

let x rep width

let height = h=x/4

let length=l= x+5

Answer 1

The volume is length times width times height=x(x+5)x/4=2500.

Multiply through by 4: x^2(x+5)=10000

x^3+5x^2-10000=0=(x-20)(x^2+25x+500). The quadratic doesn't factorise, so x=20.

Width=20cm, length=25cm, depth=5cm.