Which of the following is a true statement?
it is possible for two rectangles to have the same area, but only if they 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.
Please help! thanks.
Ms.Sue? Anyone?
You're right.
Thank you so much!!
To determine which statement is true, let's analyze each option:
Option 1: "It is possible for two rectangles to have the same area, but only if they have the same perimeter."
To check if this statement is true, we need to consider the relationship between the area and perimeter of rectangles. The area of a rectangle is determined by multiplying its length and width, while the perimeter is the sum of all the sides. It is not necessary for two rectangles to have the same perimeter in order to have the same area. Therefore, option 1 is not true.
Option 2: "It is possible for two rectangles to have the same area without having the same perimeter."
This statement aligns with our understanding. Two rectangles can have the same area even if their perimeters are different. For example, one rectangle could have dimensions of 3 units by 4 units (area = 12 square units), while another rectangle could have dimensions of 2 units by 6 units (area = 12 square units). Thus, option 2 is true.
Option 3: "It is possible for two squares to have the same area without having the same perimeter."
This statement is irrelevant to the question, as we are discussing rectangles, not squares. We can't determine its validity based on the given information.
Option 4: "It is possible for two squares to have the same perimeter without having the same area."
Again, this statement is unrelated to rectangles. However, if we consider two squares with different side lengths, they can indeed have the same perimeter but different areas. For instance, a square with a side length of 4 units will have a perimeter of 16 units, while another square with a side length of 8 units will also have a perimeter of 16 units, but their areas will be 16 square units and 64 square units, respectively. Thus, option 4 is also true.
In conclusion, the true statement among the options provided is: "It is possible for two rectangles to have the same area without having the same perimeter" (Option 2).