Let's calculate the perimeter and area of both rectangles.
The area is the product of width and height, while the perimeter is the sum of the lengths of the 4 sides.
For the first rectangle with width = 6cm and height = 6cm:
[tex]\begin{gathered} \text{Area}=(6\operatorname{cm})\cdot(6\operatorname{cm}) \\ \text{Area}=36\operatorname{cm}^2 \end{gathered}[/tex]For the perimeter we add up all the 4 sides, 6cm long each:
[tex]\begin{gathered} \text{Perimeter}=6\operatorname{cm}+6\operatorname{cm}+6\operatorname{cm}+6\operatorname{cm} \\ \text{Perimeter}=24\operatorname{cm} \end{gathered}[/tex]For the second rectangle, we follow exactly the same process.
The area is the product between 4cm (its width) and 9cm (its height):
[tex]\begin{gathered} \text{Area}=(4\operatorname{cm})\cdot(9\operatorname{cm}) \\ \text{Area}=36\operatorname{cm}^2 \end{gathered}[/tex]For the perimeter, we have two sides of length 4cm (top and bottom sides), and the other 2 with length 9cm (left and right sides). Then, its perimeter is:
[tex]\begin{gathered} \text{Perimeter}=4\operatorname{cm}+4\operatorname{cm}+9\operatorname{cm}+9\operatorname{cm} \\ \text{Perimeter}=8\operatorname{cm}+18\operatorname{cm} \\ \text{Perimeter}=26\operatorname{cm} \end{gathered}[/tex]Then:
Rectangle 1:
Area = 36 square centimeters.
Perimeter = 24 centimeters.
Rectangle 2:
Area = 36 square centimeters.
Perimeter = 26 centimeters.
Then, both rectangles have the same area, but they don't have the same perimeter.
The correct option is A). Same area only.
