A box that has a length of 2x+2 and width of x-2 has a perimeter of 90 centimeters. If the height of the box is x, what is the volume of the box?

Question

usa test prep algebra question about volume of a box. Box with a length of 2x+2, width of X-2 has a perimeter of 90. Height of box is x. Find volume.

Answer 1

The perimeter of the box is two times the length plus two times the width.  We know this is 90cm so

2(2x + 2) + 2(x-2) = 90

4x+4+2x-4 = 0-

6x = 90

x = 15

 

From there, you can find the length and the width and height by substituting in for x.  Lastly, the volume is the product of the three of those and you will have your answer.

Answer 2

Perimeter of a figure is the sum of the lengths of all sides. there are 4 lengths, 4 widths and 4 heights.

 

90 = 4*(2*X+2  + X -2 + X)     90/4 = 4*X    X= 90/16  

Length = 2*(90/16)+2   Width = (90/16)- 2  Height = 90/16  

 

Volume = Length * Width * Height Volume = 155.5