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

Mathematics

Tanya Ramsey

25 December, 09:22

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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Mckenzie Pena · 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.