Question

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?

Answer 1

To calculate the volume of the box, first solve for x using the perimeter to find the dimensions. With x=15 cm, the box dimensions are 32 cm by 13 cm by 15 cm, leading to a volume of 6240 cubic centimeters.

Step-by-step explanation:

The student is asking about the volume of a rectangular box. To find the volume, we need to use the box dimensions: length (2x + 2), width (x - 2), and height (x). The perimeter provided, which is 90 centimeters, applies to the sum of all four sides of the rectangular base (2 lengths and 2 widths). We can express it mathematically as 2(length + width).

First, we need to find the value of x by setting up and solving the equation for the perimeter:

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

2(3x) = 90

6x = 90

x = 90 / 6

x = 15

Now that we have the value of x, we can use it to find the dimensions and calculate the volume of the box:

Length: 2(15) + 2 = 32 cm

Width: 15 - 2 = 13 cm

Height: 15 cm

Volume: Length × Width × Height = 32 cm × 13 cm × 15 cm

Volume = 6240 cubic centimeters

Answer 2

First find the value of X from the perimeter given
Perimeter = L*W
90 = 2 ((2x+2) + (x-2))
90 = 4x + 4 +4x - 4
90 = 8x
x = 11.25
Length = 2x + 2
2 (11.25) +2
=24.5
Width = x-2
11.25 -2
=9.25
h =x
= 11.25

Volume = L*W*H
24.5 * 9.25 * 11.25
2549.53 units^3