Question

drag each rectangle to the category that describes it. rectangles may go in one, both, or neither category
area of 24 square units
perimeter of 20 units

Explanation:

Step1: Recall formulas for area and perimeter of a rectangle

For a rectangle with length \( l \) and width \( w \), area \( A = l \times w \), perimeter \( P = 2(l + w) \).

Step2: Analyze first rectangle (6, 4)

• Area: \( 6 \times 4 = 24 \) square units.
• Perimeter: \( 2(6 + 4) = 20 \) units. So it belongs to both categories.

Step3: Analyze second rectangle (8, 3)

• Area: \( 8 \times 3 = 24 \) square units.
• Perimeter: \( 2(8 + 3) = 22 \) units. So it belongs to "Area of 24 square units" only.

Step4: Analyze third rectangle (7, 4)

• Area: \( 7 \times 4 = 28 \) square units.
• Perimeter: \( 2(7 + 4) = 22 \) units. So it belongs to neither category.

Step5: Analyze fourth rectangle (5, 5)

• Area: \( 5 \times 5 = 25 \) square units.
• Perimeter: \( 2(5 + 5) = 20 \) units. So it belongs to "Perimeter of 20 units" only.

Answer:

• "Area of 24 square units": Rectangle with (6,4), Rectangle with (8,3)
• "Perimeter of 20 units": Rectangle with (6,4), Rectangle with (5,5)
• "Both": Rectangle with (6,4)
• "Neither": Rectangle with (7,4)

(To present as per drag - and - drop: Drag the rectangle with length 6 and width 4 to both categories; drag the rectangle with length 8 and width 3 to "Area of 24 square units"; drag the rectangle with length 5 and width 5 to "Perimeter of 20 units"; drag the rectangle with length 7 and width 4 to neither category.)