If rectangle ABCD has a larger area than rectangle EFGH, does it follow that ABCD must have a perimeter larger than that of EFGH?

Why or why not.

No

counterexample:
suppose you have a rectangle 10 by 12
Area = 120
Perimeter is 44

another rectangle 2 by 24
area = 48
perimeter = 52

Thanks! That makes a lot of sense!

32/100=16/50=8/25?

Is this the correct way to write 32% as a reduced fraction

To determine whether rectangle ABCD must have a larger perimeter than rectangle EFGH if ABCD has a larger area, let's break down the problem.

1. Area of a rectangle: The area of a rectangle can be found by multiplying its length and width, given by the formula A = length × width.
2. Perimeter of a rectangle: The perimeter of a rectangle can be calculated by adding up the lengths of all four sides, given by the formula P = 2(length + width).

Now, let's consider two scenarios:

1. If ABCD has a larger area than EFGH:
- Let's assume ABCD has a length of L1 and a width of W1, and EFGH has a length of L2 and a width of W2.
- If A1 (area of ABCD) > A2 (area of EFGH), then we can state that L1 × W1 > L2 × W2.

It's important to note that the length and width of both rectangles can vary independently, given that their areas are different. Therefore, we cannot conclusively determine if the perimeter of ABCD is larger than that of EFGH based solely on the comparison of their areas.

2. Counterexample to disprove the claim:
- Consider one rectangle with a length of 10 and a width of 5, resulting in an area of 50.
- Now, let's take another rectangle with a length of 15 and a width of 1, resulting in an area of 15.
- In this scenario, the first rectangle has a larger area (50 > 15), but its perimeter is 30, whereas the second rectangle's perimeter is 32.
- This counterexample disproves the claim that if a rectangle has a larger area, then it must also have a larger perimeter.

In conclusion, it is not necessary for rectangle ABCD to have a larger perimeter than rectangle EFGH if ABCD has a larger area. The relationship between the area and perimeter of two rectangles is not directly proportional, and it is possible to find examples where a larger area does not correspond to a larger perimeter.