Which of the following is a true statement?
A. It is possible for two rectangles to have the same area, but only if they also have the same perimeter.
B. It is possible for two rectangles to have the same area without having the same perimeter.
C. It is possible for two squares to have the same area without having the same perimeter.
D. It is possible for two squares to have the same perimeter without having the same area.
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Well you know that all four sides of a square are the same length... so D is out, and C is out... since there are not two numbers that form a square that give a different area and perimeter.
So you are back to A and B...
consider a rectangle with length 12 and width 3... the area is 36
while its perimeter is 12+12+3 + 3
A rectangle with length 18 and width 2 also has an area of 36, but this perimeter is 40 units
so... is A) or B) correct ??
To determine which statement is true, we need to analyze each option:
A. It is possible for two rectangles to have the same area, but only if they also have the same perimeter.
To test this statement, we can consider two rectangles with different dimensions. For example, one rectangle could have dimensions 4 units by 3 units (perimeter = 14 units, area = 12 square units), and another rectangle could have dimensions 6 units by 2 units (perimeter = 16 units, area = 12 square units). Since the two rectangles have different perimeters but the same area, Statement A is incorrect.
B. It is possible for two rectangles to have the same area without having the same perimeter.
As shown in the previous example, two rectangles can indeed have the same area without having the same perimeter. Therefore, Statement B is correct.
C. It is possible for two squares to have the same area without having the same perimeter.
Since squares have all sides equal, if two squares have the same area, it implies they have the same side length. As a result, if they have the same side length, they will also have the same perimeter. Therefore, Statement C is incorrect.
D. It is possible for two squares to have the same perimeter without having the same area.
To test this statement, we can consider two squares with different side lengths. For example, one square could have a side length of 4 units (perimeter = 16 units, area = 16 square units), and another square could have a side length of 8 units (perimeter = 32 units, area = 64 square units). Since the two squares have the same perimeter but different areas, Statement D is correct.
Based on the analysis, the correct statement is:
B. It is possible for two rectangles to have the same area without having the same perimeter.