Is it possible that a parallelogram with length of the sides equal to 4 cm and 7 cm has the length of one of the diagonals 2 cm?

Question

Magdalena Roth

Mathematics

26 September, 09:46

Is it possible that a parallelogram with length of the sides equal to 4 cm and 7 cm has the length of one of the diagonals 2 cm?

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Answers (1)

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Juliana Owens · Answer 1

No.

Step-by-step explanation:

Two adjacent sides and a diagonal form a triangle. When the sides are 4 and 7, the triangle inequality tells you the remaining side (of the triangle) must be between 7-4 = 3 and 7+4 = 11. A diagonal length of 2 is not possible.

Another way to put this is that the sum of the two shortest sides (4 and 2, in this case) must exceed the longest side (7 in this case). That sum does not.