A rectangle having sidelengths 5 cm and 3 cm is made using a piece of wire. If the wire is straightened and then bent to form a square, what will be the length of a side of the square?
Given: Rectangle with side lengths 5 cm and 3 cm.
Step 1: Find the perimeter of the rectangle. Perimeter = 2 × (length + breadth) = 2 × (5 + 3) = = 16 cm
Step 2: The length of wire = perimeter of rectangle = 16 cm.
Step 3: When bent into a square, perimeter remains the same = 16 cm.
Step 4: For a square, perimeter = 4 × side. side = 16 ÷ 4 = 4 cm
Answer: The length of each side of the square will be 4 cm.
Explanation
The perimeter of the rectangle equals the total length of the wire. When the same wire is bent into a square, the perimeter remains the same. The perimeter of the rectangle is 2 × (5 + 3) = 16 cm. For a square, perimeter = 4 × side, so side = 16 ÷ 4 = 4 cm.
Solution Steps
Step 1: Find the perimeter of the rectangle = 2 × (length + breadth) = 2 × (5 + 3) = = 16 cm
Step 2: The length of wire = perimeter of rectangle = 16 cm
Step 3: When bent into a square, perimeter remains the same = 16 cm
Step 4: For a square, perimeter = 4 × side, so side = 16 ÷ 4 = 4 cm