Question

quadrilateral ghij is a kite. what is fj? fj =

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 \(GHIJ\) are \(IJ\) and \(GH\) which intersect at \(F\). If we assume \(GH\) bisects \(IJ\) (a common property of kites), and we know that in right - triangle \(GFJ\), we can use the Pythagorean theorem. Let the length of \(GJ = 97\) and \(GF=65\).

Step2: Apply Pythagorean theorem

In right - triangle \(GFJ\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = GJ\) and \(a = GF\), and \(b = FJ\). So \(FJ=\sqrt{GJ^{2}-GF^{2}}\).

Step3: Calculate the value

Substitute \(GJ = 97\) and \(GF = 65\) into the formula: \(FJ=\sqrt{97^{2}-65^{2}}=\sqrt{(97 + 65)(97 - 65)}=\sqrt{162\times32}=\sqrt{5184}=72\).

Answer:

72