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
