A square and a rectangle have the same area.If the side of the square is 8cm and the length of the rectangle is 16cm. What is the width of the rectangle? ?

The area of a square is calculated by squaring the length of one of its sides. In this case, the area of the square is 8cm x 8cm = 64cm^2.

Since the square and the rectangle have the same area, the area of the rectangle is also 64cm^2. The formula for the area of a rectangle is length x width. We know the length of the rectangle is 16cm, so we can plug in the values to find the width:

16cm x width = 64cm^2
width = 64cm^2 / 16cm
width = 4cm

Therefore, the width of the rectangle is 4cm.

Step 1: Calculate the area of the square

Area of square = (side)² = 8² = 64 cm²

Step 2: Since the areas are equal, set the area of the square equal to the area of the rectangle

Area of square = Area of rectangle
64 cm² = length × width

Step 3: Substitute the given length and solve for width

64 cm² = 16 cm × width
width = 64 cm² / 16 cm
width = 4 cm

Therefore, the width of the rectangle is 4 cm.