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

Answer:

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.

Step-by-step 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.