Question

Enter and solve a polynomial equation for the situation described.

A piece of granite is being cut for a building foundation. You want its length to be five times its height and its width to be six times its height. If you want the granite to be 1,920 cubic centimeters, what will its length, width, and height be? Use x for the height of the granite.

The equation is __________ .

The length of the slab will be ____ cm, the width ____ cm, and the height ____ cm.

Answer 1

Height = x (This is given)

Length = 5x

Width = 6x

Volume = length × width × height

The equation will be: (5x)(6x)(x) = 1920

simplify:

30x² × (x) = 1920

30x³ = 1920

Divide both sides by 30

x³= 64

x = ∛64

x= 4

If x = height, then, the height is 4cm

5x = length

20cm = length

6x = width

24cm = width