Question

If two squares have the same perimeter, then they have the same area.

Question 2 options:
True
False

Answer 1

The statement is **False**.

Two squares can have the same perimeter but different side lengths, which will lead to different areas.

For example, consider two squares:

1. A square with a side length of 4 units:
- Perimeter = 4 * 4 = 16 units
- Area = 4 * 4 = 16 square units

2. A square with a side length of 2 units:
- Perimeter = 4 * 2 = 8 units
- Area = 2 * 2 = 4 square units

These two squares do not have the same perimeter. However, if we have two squares with the same perimeter, we can calculate the side lengths:

If both squares have the same perimeter \( P \), then:
- For the first square, if side length is \( s_1 \): \( P = 4s_1 \); hence \( s_1 = \frac{P}{4} \)
- For the second square, if side length is \( s_2 \): \( P = 4s_2 \); hence \( s_2 = \frac{P}{4} \)

That means the side lengths will be the same if the perimeters are equal, leading to the same area. However, it is possible to create rectangles with the same perimeter that have differing areas.

Thus, the correct answer is **False**.