In parallelogram DEFG, \( \mathrm{DE}=6 \) inches and \( \mathrm{DF}=6.4 \) inches. Diagonals \( \overline{\mathrm{GE}} \) and \( \overline{\mathrm{DF}} \) intersect at point H . If \( \mathrm{GH}=4 \) inches, what is the length of \( \overline{\mathrm{GE}} \) ? \[ \mathrm{GE}=\square \text { inches } \]

In a parallelogram, the diagonals bisect each other. This means that the lengths of the segments created by the intersection of the diagonals are equal. Since \( \overline{\mathrm{GE}} \) is divided into two segments \( \overline{\mathrm{GH}} \) and \( \overline{\mathrm{HE}} \), we know that \( \overline{\mathrm{HE}} \) will also equal \( \overline{\mathrm{GH}} \). Given \( GH = 4 \) inches, we find that \( HE = 4 \) inches. Therefore, we can calculate the total length of \( \overline{\mathrm{GE}} \) by adding the lengths of \( \overline{\mathrm{GH}} \) and \( \overline{\mathrm{HE}} \): \[ GE = GH + HE = 4 + 4 = 8 \text{ inches}. \] So, the length of \( \overline{\mathrm{GE}} \) is 8 inches.