Question

Consider the following two statements about the rectangles a student draws.
Statement 1: Rectangles have the same perimeter.
Statement 2: Rectangles have the same area.
Which of the following statements is sufficient to conclude that the rectangles are congruent?
a. Statement 1 alone is sufficient, but statement 2 alone is not sufficient.
b. Statement 2 alone is sufficient, but statement 1 alone is not sufficient.
c. Both statements together are sufficient, but neither statement alone is sufficient.
d. Both statements together are not sufficient.

Answer 1

Answer:

C.

Step-by-step explanation:

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Answer 2

Solution:

Know that both statement 1 and statement 2 are true for concluding that the given rectangles are congruent.

Understand that, individually they are not sufficient to to conclude that the two rectangles are congruent.

As, if two rectangle having different dimensions will have same perimeter by their area are may not be the same similarly two rectangles having same areas may or may not have same perimeter.

Therefore, Both statements together are sufficient, but neither statement alone is sufficient.

Hence, the correct answer is option (c).