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

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

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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