A rectangular park having twice length of the breadth. A half pathway width of 4 cm having area of is 352 m². Find the length of the rectangular park (in meters)?

To find the length of the rectangular park, we can break down the problem step-by-step:

Step 1: Define the variables for the park's dimensions
Let the breadth of the rectangular park be represented by $b$ meters.
Since the length of the park is twice its breadth, the length ($l$) can be expressed as:

$l=2b$

Step 2: Understand the pathway dimensions and area
The problem mentions a "half pathway" of width $4\text{m}$ (noting that "4 cm" in the question is a typographical unit error, as the area is in square meters) with an area of $352{\text{m}}^2$.
A "half pathway" refers to a pathway constructed along only one of the breadth sides of the rectangular park.
The area of this pathway is calculated by multiplying the breadth of the park by the width of the path:

$\text{Area of the pathway}=\text{Breadth}\left(b\right)\times \text{Pathway Width}$

Step 3: Set up the equation and solve for the breadth ($b$)
Substituting the given values into the equation:

$352=b\times 4$

$b=\frac{352}{4}$

$b=88\text{meters}$

Step 4: Calculate the length of the rectangular park
Now, substitute the value of $b$ back into our expression for the length:

$l=2\times 88$

$l=176\text{meters}$

Thus, the length of the rectangular park is 176 meters.