Question

The Area and the Perimeter of the following rectangle are equal. Find x, the length of the rectangle, the Area and Perimeter. The length of the rectangle is 12x and the height is 3 ft.

Answer 1

x =
`(1)/(2)`

Explanation:

First, let's figure out the full perimeter, which is easy. We know the general length and height, so we multiply that by 2.

2(12x + 3) = 24x + 6.

The perimeter is 24x + 6 so far, as we don't know the value of x yet. Given in the question, the area and perimeter are equal. As we know, the area is length multiplied by the height/width. To figure out x, let's compare the perimeter to the area.

24x + 6 = 12x(3)
24x + 6 = 36x

Now we have an equation that compares the area to the perimeter. Let's solve for x.

24x + 6 = 36x
6 = 12x Subtracted 24x from both sides

`(1)/(2)` = x Divided 12 from both sides

Now we know that x equals
`(1)/(2)`. Let's plug it in to make sure.

24(
`(1)/(2)`) + 6 = 36(
`(1)/(2)`)
12 + 6 = 18