Recognize that rectangles that have the same area can have different perimenters.

Do rectangles with the same area necessarily have the same perimeter?Give an example to support your answer.

How I would handle this is to first look at the formula.

Area=Length*Width

Make up a rectangle's length and width. Let's say 5 feet and 3 feet.

A = 5ft * 3ft

The area is 15 sq feet.

Make sense so far?

Now, we have the following equation to make up another area with.

15 = Length*Width

Put a number value (other than 5 or 3) in for the length. Then solve for the width. Or put a value in for the width--then solve for the length. Whichever :)

Matt

To answer the question, we can use the formula for the area of a rectangle, which is length multiplied by width. Let's start with an example where the length is 5 feet and the width is 3 feet. Using the formula, we can calculate the area:

Area = Length * Width = 5 ft * 3 ft = 15 sq ft.

So, the area of this rectangle is 15 square feet.

Now, let's consider another rectangle with the same area (15 square feet), but different dimensions. We can use the equation:

15 sq ft = Length * Width

To find a different set of length and width values, we can choose a random value for one of the variables and then solve for the other. For example, let's choose a value of 6 feet for the length:

15 sq ft = 6 ft * Width

To find the value of Width, we can divide both sides of the equation by 6 ft:

15 sq ft / 6 ft = Width

Width ≈ 2.5 ft

Therefore, we have found another set of dimensions for a rectangle with an area of 15 square feet. The length is 6 feet and the width is approximately 2.5 feet.

As you can see, even though both rectangles have the same area, their perimeters are different because their dimensions (length and width) are different. This example illustrates that rectangles with the same area do not necessarily have the same perimeter.