Question

The length is 3 inches more than the width period the width is 2 inches more than the height. The volume is 120 in.³. What is the dimensions of the box

Answer 1

Answer:

the dimension of the box is : 8 by 5 by 3

Length = 8

Width = 5

Height = 3

Step-by-step explanation:

Let x,y and z represent the length, width and height of the box.

Given;

The length is 3 inches more than the width

x = y+3 .......1

the width is 2 inches more than the height

y = z + 2

z = y-2 .........2

Volume = length×width×height = xyz = 120 in^3

xyz = 120 ........3

Substituting equation 1 and 2 into 3

(y+3)×y ×(y-2) = 120

y(y^2+y-6) = 120

y^3 + y^2 - 6y - 120 = 0

Solving the polynomial equation we have;

y = 5

From equation 1;

x = y+3 = 5+3

x = 8

From equation 2;

z = y-2 = 5-2

z = 3

Therefore, the dimension of the box is

8 by 5 by 3

Length = 8

Width = 5

Height = 3