Question

Do the following rectangles have the same perimeter, area, or both?6 cmUS6 cm4 cm9 cmChoose 1 answer:Same area onlySame perimeter onlySame area and perimeter

Answer 1

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:

$\begin{gathered} \text{Area}=(6\operatorname{cm})\cdot(6\operatorname{cm}) \\ \text{Area}=36\operatorname{cm}^2 \end{gathered}$

For the perimeter we add up all the 4 sides, 6cm long each:

$\begin{gathered} \text{Perimeter}=6\operatorname{cm}+6\operatorname{cm}+6\operatorname{cm}+6\operatorname{cm} \\ \text{Perimeter}=24\operatorname{cm} \end{gathered}$

For the second rectangle, we follow exactly the same process.

The area is the product between 4cm (its width) and 9cm (its height):

$\begin{gathered} \text{Area}=(4\operatorname{cm})\cdot(9\operatorname{cm}) \\ \text{Area}=36\operatorname{cm}^2 \end{gathered}$

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:

$\begin{gathered} \text{Perimeter}=4\operatorname{cm}+4\operatorname{cm}+9\operatorname{cm}+9\operatorname{cm} \\ \text{Perimeter}=8\operatorname{cm}+18\operatorname{cm} \\ \text{Perimeter}=26\operatorname{cm} \end{gathered}$

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.