Question

If both the square and rectangle have the same area, which figure has larger perimeter?


? 16 inches

• A. cannot be determined
• B. both have the same perimeter
• C. rectangle
• D. square

Answer 1

The correct option is C rectangle

$\text{Area of square is equal to}$ $\text{the area of the rectangle.}$

$\text{Let's find the area of square first.}$

Area of square = side x side = 8 in x 8 in = 64 sq in
$\therefore \text{Area of square = 64 sq in}$

$\therefore \text{Area of Rectangle = 64 sq in}$

$\text{Now, let's find the width of Rectangle.}$

Area of rectangle = length x breadth
64 sq in = 16 in x breadth
breadth = 64 / 16 = 4 in
$\text{Hence, the width of rectangle B is 4 in.}$

Perimeter of square = 4 x side = 4 x 8 = 32 in
Perimeter of rectangle = 2 x (length + breadth)
= 2 x (16 + 4) = 2 x 20 = 40 in