Question : Each side of a square is 12 cm long. The perimeter of this square is equal to the perimeter of a rectangle whose length is 16 cm. What will be the area of this rectangle?
Option 1: 128 cm2
Option 2: 112 cm2
Option 3: 184 cm2
Option 4: 156 cm2
Correct Answer: 128 cm 2
Solution :
The side of a square = 12 cm
Length of the rectangle = 16 cm
Perimeter of the square = 4 × side = 4 × 12 = 48 cm
The perimeter of a rectangle = 48 cm (since it is equal to the perimeter of the square)
Let's assume the width of the rectangle to be 'w'.
Perimeter of rectangle = 2 × (length + width)
⇒ 48 = 2 × (16 + w)
⇒ 24 = 16 + w
$\therefore$ w = 24 – 16 = 8
Therefore, the width of the rectangle is 8 cm.
The area of the rectangle can be calculated as:
Area of rectangle = length × width = 16 × 8 = 128 cm
2
Hence, the correct answer is 128 cm
2
.
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