Question

A rectangle has a fun property. The value of its perimeter is equal to the value of its area. The rectangle has a length of 2x feet and a width of 3 feet. 1. Write the equation perimeter equals to the area. 2. Solve for 'x' 3. Write both the value of the perimeter and the value of the area.

Answer 1

1)
`6\cdot x = 4\cdot x+6`, 2) The value of
`x` is 3, 3) The perimeter and the area of the rectangule are 18 feet and 18 square feet, respectively.

Explanation:

Let be a rectangle with a length of
`2\cdot x` feet and a width of 3 feet. The area (
`A`), measured in square feet, and perimeter (
`p`), measured in feet, formulas are, respectively:

`A = (2\cdot x)\cdot (3)`

`A = 6\cdot x` (Eq. 1)

`p = 4\cdot x + 6` (Eq. 2)

1) Now, we assume that
`p = A`, then we reduce the system of linear equation into a sole linear equation:

`6\cdot x = 4\cdot x+6` (Eq. 3)

2) We proceed to solve for
`x`:

`2\cdot x = 6`

`x = 3`

The value of
`x` is 3.

3) Lastly, we obtain the values of the perimeter and area:

`A = 6\cdot (3)`

`A = 18\,ft^(2)`

`p = 4\cdot (3)+6`

`p = 18\,ft`

The perimeter and the area of the rectangule are 18 feet and 18 square feet, respectively.