Question

| more on inequalities in triangles. theorems.
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it is possible that in a parallelogram with side lengths of 4 cm and 7 cm, the length of one of the diagonals is 2 cm?
answer: it is

Explanation:

Step1: Recall triangle - inequality in parallelogram

In a parallelogram, the two adjacent sides and a diagonal form a triangle. Let the side - lengths of the parallelogram be \(a = 4\mathrm{cm}\) and \(b = 7\mathrm{cm}\), and the diagonal be \(d\).

Step2: Apply the triangle - inequality theorem

The triangle - inequality theorem states that for a triangle with side - lengths \(x\), \(y\), and \(z\), \(x + y>z\), \(x+z > y\), and \(y + z>x\). In the triangle formed by two adjacent sides of the parallelogram and a diagonal, if \(a = 4\), \(b = 7\), and \(d\) is the diagonal, then \(|a - b|

Step3: Calculate the range of the diagonal length

Substitute \(a = 4\) and \(b = 7\) into the inequality \(|a - b|

Answer:

It is not possible.