Question

One of the sides of a parallelogram has the length of 5 in. can the lengths of the diagonals be: c 6 in and 7 in?

Answer 1

The dimensions of 5 inches for a side and diagonals of 6 inches and 7 inches for a parallelogram violate the Pythagorean theorem and therefore are not possible for any right-angled triangle, suggesting an error if considered for a parallelogram.

Step-by-step explanation:

The question is whether parallelogram sides can correspond to the dimensions given, with one side being 5 inches and the possible diagonals being 6 inches and 7 inches respectively. By applying the Pythagorean theorem, we can deduce that a parallelogram with such dimensions may not be possible due to the constraints of the theorem.

Given the Pythagorean theorem, expressed as a² + b² = c², the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. If we consider the diagonals and the side as parts of a right triangle, then 6² + 5² does not equal 7² (36 + 25 = 61, which is not equal to 49).

Therefore, it is not possible for a parallelogram to have side lengths and diagonal lengths as described in the question because the mathematically described conditions violate the rules of the Pythagorean theorem.

Answer 2

Answer: Yes, the diagonals could be 6 and 7 in.

In a parallelogram, only the opposite sides of the parallelogram are congruent. All the sides don't have to be congruent. Therefore we can have different measurement for the diagonals.

In a square, all of the diagonals would have to be the same.