Question

The length of a rectangle is $4x + 3$ and the width is $2x - 6$ , how do you write the expression for the perimeter of the rectangle?

Answer 1

Hint: For solving this particular problem we just have to take the sum of the twice the length of the rectangle and twice the width of the rectangle, Where ,$p$ is representing the perimeter of the rectangle , $l$ is the length of the rectangle , and $w$ is the width of the rectangle.

Complete step by step solution:
It is given that ,
The length of a rectangle is $4x + 3$ , and
The width of the rectangle is $2x - 6$.
By definition we already knew that the perimeter of an object is equal to the length of all its sides.
We also know that , for a shape like a rectangle the opposite sides of the rectangle are equal.
Therefore, we can write the equation for the perimeter of the rectangle can be written as:
Perimeter is equal to the sum of the twice the length of the rectangle and twice the width of the rectangle , that can be represented as,
$p = 2l + 2w$
Where,
$p$ is representing the perimeter of the rectangle ,
$l$ is the length of the rectangle , and
$w$ is the width of the rectangle.
Now, substitute the given values in $p = 2l + 2w$,
We will get the following expression,
$ \Rightarrow p = 2(4x + 3) + 2(2x - 6)$
$ \Rightarrow p = 8x + 6 + 4x - 12$
$ \Rightarrow p = 12x - 6$
Hence, we get the required result.

Note: The solution of the addition or subtraction between two numbers will have the sign of the greater number. If there's subtraction between a positive and a negative number then there's addition.