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Answer :
Final answer:
The dimensions of the box are 5 inches in width, 8 inches in length, and 3 inches in height.
Explanation:
Let's assign variables to the dimensions of the box: width = w, length = w + 3, height = w - 2. We can then use the formula for volume to set up an equation:
V = w(w + 3)(w - 2) = 120
Expanding and simplifying the equation:
w³ + w² - 6w - 120 = 0
Using numerical methods or factoring, we can find that w = 5. Now we can substitute this value into the expressions for length and height:
Width = 5 inches
Length = 5 + 3 = 8 inches
Height = 5 - 2 = 3 inches
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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
