Question

Is it possible that in a parallelogram with side lengths of 4 cm and 7 cm, the length of one of the diagonals is 2 cm?

a) Yes, it is possible.
b) No, it is not possible.

Answer 1

In a parallelogram, the lengths of opposite sides are equal. Using the formula for the length of the diagonal, we can determine that the length of one of the diagonals cannot be 2 cm. The correct answer is No, it is not possible (b).

Step-by-step explanation:

In a parallelogram, the lengths of opposite sides are equal. Therefore, if the side lengths of the parallelogram are 4 cm and 7 cm, then the opposite sides are also 4 cm and 7 cm.

Since the length of a diagonal of a parallelogram is the square root of the sum of the squares of the two opposite sides, we can calculate the length of the diagonals of the parallelogram using the formula:

Length of Diagonal = √(Side1^2 + Side2^2)

= √(4^2 + 7^2)

= √65

≈ 8.06 cm

Therefore, the length of one of the diagonals cannot be 2 cm. The correct answer is No, it is not possible (b).