Question

quadrilateral efgh is a kite. what is dg? dg =

Explanation:

Step1: Recall kite - property

In a kite, the diagonals are perpendicular and one diagonal is bisected by the other. Let's assume the diagonals of the kite \(EFGH\) are \(EG\) and \(FH\) which intersect at \(D\). We know that in right - triangle \(DFG\), we can use the Pythagorean theorem.

Step2: Apply Pythagorean theorem

In right - triangle \(DFG\), if we let \(DF = 16\) and \(FG=34\), and we want to find \(DG\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = FG\), \(a = DF\), and \(b = DG\). So \(DG=\sqrt{FG^{2}-DF^{2}}\).

Step3: Substitute values

Substitute \(FG = 34\) and \(DF = 16\) into the formula: \(DG=\sqrt{34^{2}-16^{2}}=\sqrt{(34 + 16)(34 - 16)}\) (using the difference - of - squares formula \(a^{2}-b^{2}=(a + b)(a - b)\)). Then \(DG=\sqrt{50\times18}=\sqrt{900}=30\).

Answer:

30