7. Which of the following is a true statement? (1 point)
It is possible for two rectangles to have the same area, but only if they also have the same
perimeter.
It is possible for two rectangles to have the same area without having the same perimeter.
It is possible for two squares to have the same area without having the same perimeter.
It is possible for two squares to have the same perimeter without having the same area.
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1: B
2 :B
3: C
4: D
5: B
6: A
7: C
8: C
9: A
10: B
11: C
12: B
13: D
14: C
15: A
16: C
17: D
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awnsers please Which of the following is a true statement?
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To determine which statement is true, let's consider the properties of rectangles and squares.
1. It is possible for two rectangles to have the same area, but only if they also have the same perimeter. This statement is NOT true. Rectangles with different perimeters can have the same area. For example, a rectangle with dimensions 2x3 and another with dimensions 1x6 have different perimeters (10 vs. 14), but they both have an area of 6.
2. It is possible for two rectangles to have the same area without having the same perimeter. This statement is TRUE. As mentioned in the previous example, rectangles with different perimeters can have the same area.
3. It is possible for two squares to have the same area without having the same perimeter. This statement is NOT true. Squares with different perimeters cannot have the same area. Since all sides of a square are equal, if two squares have different perimeters, their side lengths would be different, resulting in different areas.
4. It is possible for two squares to have the same perimeter without having the same area. This statement is TRUE. Two squares can have the same perimeter but different areas. For example, a square with side length 5 has a perimeter of 20 and an area of 25, while another square with side length 8 also has a perimeter of 20 but has an area of 64.
Therefore, based on the explanations above, the correct statement is: "It is possible for two rectangles to have the same area without having the same perimeter."