A rectangular box has a perimeter of 36 inches. Which of the following equations represents the area of the rectangular box in terms of its width, w?
a. A = 36w - w2
b. A = 18w - w2
c. A = 36 - w2
d. A = 18 - w2
let the length be l
let the width be w
so 2l + 2w = 36
l + w = 18
l = 18-w
area = wl
= w(18-w)
= 18w - w^2
To find the equation representing the area of the rectangular box in terms of its width, we first need to understand the relationship between the width, length, and perimeter of a rectangle.
The perimeter of a rectangle is found by adding up the lengths of all its sides. For a rectangular box, there are two sides of length w (width) and two sides of length l (length). The perimeter is then given by the equation:
perimeter = 2w + 2l
Since we know the perimeter of the box is 36 inches, we can write the equation as:
36 = 2w + 2l
To find the area of the rectangular box, we multiply the width by the length:
area = w * l
Now, we need to rearrange the equation for the perimeter to solve for l:
36 = 2w + 2l
36 - 2w = 2l
18 - w = l
Substituting the expression for l into the area equation, we get:
area = w * l
area = w * (18 - w)
Expanding the equation, we have:
area = 18w - w^2
Therefore, the correct equation representing the area of the rectangular box in terms of its width is:
A = 18w - w^2
Therefore, the correct answer is option b: A = 18w - w^2.