Question

type the correct answer in the box. use numerals instead of words.
in parallelogram defg, de = 6 inches and df = 6.4 inches. diagonals \\( \overline { g e } \\) and \\( \overline { d f } \\) intersect at point h. if gh = 4 inches, what is the length of \\( \overline { g e } \\)?
\\( g e = \\) inches
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Explanation:

Step1: Recall the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So, if diagonals \( \overline{GE}\) and \( \overline{DF}\) intersect at point \(H\), then \(GH = HE\).

Step2: Calculate the length of \(GE\)

Since \(GH = 4\) inches and \(GE=GH + HE\), and \(GH = HE\) (by the property of parallelogram diagonals), then \(GE = 2\times GH\).
Substitute \(GH = 4\) into the formula: \(GE=2\times4\).

Answer:

\(8\)