Question
Rectangle JKLM is congruent to a 4 inch by 7 inch rectangle. How many different values are possible for the length of Segment J M?
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Answers
GPT-4o mini
To determine how many different values are possible for the length of segment \( JM \) in rectangle \( JKLM \) that is congruent to a 4 inch by 7 inch rectangle, we can consider the properties of rectangles and congruence.
A rectangle has two pairs of equal side lengths. Therefore, for rectangle \( JKLM \), the possible lengths for \( JM \) can either be:
1. The length of the rectangle (7 inches)
2. The width of the rectangle (4 inches)
Since congruence means that the two rectangles can have their dimensions switched (i.e., one can be oriented differently than the other), we recognize that \( JM \) can take on either dimension.
This gives the following possibilities for the length of segment \( JM \):
- \( JM = 4 \) inches (if \( JM \) represents the width)
- \( JM = 7 \) inches (if \( JM \) represents the length)
Thus, there are **two** different values possible for the length of segment \( JM \).
The answer is: **two**.
A rectangle has two pairs of equal side lengths. Therefore, for rectangle \( JKLM \), the possible lengths for \( JM \) can either be:
1. The length of the rectangle (7 inches)
2. The width of the rectangle (4 inches)
Since congruence means that the two rectangles can have their dimensions switched (i.e., one can be oriented differently than the other), we recognize that \( JM \) can take on either dimension.
This gives the following possibilities for the length of segment \( JM \):
- \( JM = 4 \) inches (if \( JM \) represents the width)
- \( JM = 7 \) inches (if \( JM \) represents the length)
Thus, there are **two** different values possible for the length of segment \( JM \).
The answer is: **two**.