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?

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.

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AFOKE88 AFOKE88 · Answer 2 · 2021-09-24T15:37:45+02:00

No, it's not possible for one of the diagonals to be 2 cm.

A parallelogram has 4 sides and as such the diagonal will cut the parallelogram into 2 triangles.

This means that 2 adjacent sides of the parallelogram will be 2 sides of each the triangles.

Now, our 2 adjacent sides are 4 cm and 7cm.

Since the third side of the triangle which is the diagonal of the parallelogram is unknown, we can have an idea of the range of the diagonal by using a theorem known as the Triangle inequality theorem. This theorem states that the sum of any two sides of any triangle is greater than or equal to the third side.

Applying that to our question, it means that if the diagonal is x, then we can say that; 7 + 4 ≥ x

Thus; 11 ≥ x

Now, it means 2cm can't be the length of one of the diagonals because we have seen that it is greater than or equal to 11 cm.

Read more at; brainly.com/question/24512960