Question

1. if de = 16x - 3, hi = 9x + 11, and df = 52, find hg.

Explanation:

Step1: Find the value of \(x\)

Since \(DE = 16x - 3\), \(HI=9x + 11\), and \(DE = HI\) (property of the figure, assuming it's a rhombus or a figure with equal - length sides in a certain relation).

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Step2: Find the length of \(HG\)

Given \(DF = 52\), and assuming the figure is a rhombus (diagonals bisect each other). If \(DF\) is a diagonal and \(HG\) is related to the other diagonal (assuming the other diagonal is bisected in the same way as the given one). Since \(x = 2\), and if \(HG\) has the same length as \(HI\) (by symmetry of the figure, for example, if it's a rhombus \(HI = HG\)). Substitute \(x = 2\) into \(9x+11\).

$$HG=9x + 11=9\times2+11=18 + 11=29$$

Answer:

\(29\)