Final answer:
To find the perimeter of the original rectangle, we need the specific measurements of length and width, which are not provided. The increase in perimeter is 9 meters, based on the 13m² increase in area when each dimension is increased by 2 meters.
Step-by-step explanation:
The question asks to determine the perimeter of a rectangle given that the area increases by 13m² when both the width and length are increased by 2 meters. We can create two equations based on the given information. The original area of the rectangle can be represented as A = lw (where l is the original length and w is the original width), and the new area after the increase can be represented as (l + 2)(w + 2). The increase in area is then written as (l + 2)(w + 2) - lw = 13.
Expanding the equation and simplifying, we get:
lw + 2l + 2w + 4 - lw = 13
This simplifies to:
2l + 2w + 4 = 13
By subtracting 4 from both sides, we have:
2l + 2w = 9
This equation represents the combined increase in length and width, which can also be seen as the increase in the perimeter. Therefore, the increase in perimeter is 9 meters. The original perimeter can be found using the perimeter formula P = 2l + 2w. So, if we increase the original perimeter by 9 meters, we can find the new perimeter:
P + 9 = New Perimeter
However, we cannot find the exact value of the original perimeter without the specific measurements of length and width. Instead, we can respond that the perimeter is increased by 9 meters due to the enlargement of each dimension by 2 meters.