In the image, you are tasked with drawing a rectangle that has the same perimeter as the one shown but with a larger area.

Step-by-step solution:

1. Identify the dimensions of the current rectangle:

   • The top rectangle is a 5x2 rectangle.
   • This means it has a width of 5 units and a height of 2 units.

2. Calculate the perimeter of the original rectangle: The formula for the perimeter $P$ of a rectangle is: $P = 2 \times (\text{length} + \text{width})$ For the 5x2 rectangle: $P = 2 \times (5 + 2) = 2 \times 7 = 14 \text{ units}$

3. Find a new rectangle with the same perimeter: The new rectangle must have the same perimeter of 14 units but a larger area. We will try different pairs of length and width that satisfy this condition.

   For example:

   • If the length is 4 units, then the width must be $3$ units because: $2 \times (4 + 3) = 14$ So a 4x3 rectangle also has a perimeter of 14 units.

4. Calculate the area of both rectangles:

   • The area of the original 5x2 rectangle is: $A = 5 \times 2 = 10 \text{ square units}$
   • The area of the new 4x3 rectangle is: $A = 4 \times 3 = 12 \text{ square units}$

Thus, a 4x3 rectangle has the same perimeter (14 units) but a greater area (12 square units compared to 10 square units).

Would you like further clarification on any part of this process?

Here are 5 related questions to deepen your understanding:

1. What other dimensions could result in a rectangle with a perimeter of 14 units?
2. Why does the perimeter remain constant, even though the area changes?
3. Can you find the dimensions of a square with the same perimeter of 14 units?
4. What is the relationship between area and perimeter for different shapes?
5. How does increasing the dimensions of one side affect the area of a rectangle?

Tip: When maximizing the area with a fixed perimeter, a square often gives the maximum possible area.