Question

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

6 \t\t\t\t\t\t\t\t\t\t\t8 \t\t\t\t\t\t\t\t\t\t\t7 \t\t\t\t\t\t\t\t\t\t\t5
4 \t\t\t\t\t\t\t\t\t\t\t3 \t\t\t\t\t\t\t\t\t\t\t4 \t\t\t\t\t\t\t\t\t\t\t5

Explanation:

Step1: Recall formulas

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: \( 2(6 + 4)=2\times10 = 20 \) units. So it belongs to both.

Step3: Analyze second rectangle (8,3)

• Area: \( 8 \times 3 = 24 \) square units.
• Perimeter: \( 2(8 + 3)=2\times11 = 22 \) units. So it belongs to "Area of 24 square units".

Step4: Analyze third rectangle (7,4)

• Area: \( 7 \times 4 = 28 \) square units.
• Perimeter: \( 2(7 + 4)=2\times11 = 22 \) units. So it belongs to neither.

Step5: Analyze fourth rectangle (5,5) (square, a type of rectangle)

• Area: \( 5 \times 5 = 25 \) square units.
• Perimeter: \( 2(5 + 5)=2\times10 = 20 \) units. So it belongs to "Perimeter of 20 units".

Answer:

• Rectangle with length 6, width 4: Both "Area of 24 square units" and "Perimeter of 20 units".
• Rectangle with length 8, width 3: "Area of 24 square units".
• Rectangle with length 7, width 4: Neither.
• Rectangle with length 5, width 5: "Perimeter of 20 units".