Respuesta :
Answer:
To find the perimeter of a rectangle when given its area, we need to use the formula for the area of a rectangle and then use that information to find the perimeter.
The formula for the area of a rectangle is:
Area
=
Length
×
Width
Area=Length×Width
Given that the area of the rectangle is 30 m², let's denote the length of the rectangle as
�
l meters and the width as
�
w meters. So, we have:
�
�
=
30
lw=30
To find the perimeter (
�
P) of the rectangle, we use the formula:
�
=
2
�
+
2
�
P=2l+2w
We can solve the area equation for one of the variables (either
�
l or
�
w) and then substitute it into the perimeter formula.
Let's solve the area equation for
�
l:
�
=
30
�
l=
w
30
Now, we'll substitute
�
l into the perimeter formula:
�
=
2
(
30
�
)
+
2
�
P=2(
w
30
)+2w
�
=
60
�
+
2
�
P=
w
60
+2w
To find the minimum or maximum value of
�
P, we can use calculus by finding the critical points. However, since you haven't specified any constraints on the rectangle (such as fixed aspect ratio), the perimeter can theoretically approach infinity. So, without additional constraints, we can't determine a specific value for the perimeter.
Step-by-step explanation:
