Question

find the missing length of cd in kite abcd. the missing length of cd is . (type an integer or a decimal.)

Explanation:

Step1: Recall kite - property

In a kite, the diagonals are perpendicular. Let the intersection of the diagonals of kite \(ABCD\) be point \(E\). The diagonals of a kite are perpendicular bisectors of each other. Let \(AC\) and \(BD\) be the diagonals. We know that \(AC = 18\) and \(BD=24\), and they are perpendicular at \(E\).

Step2: Use the Pythagorean theorem

In right - triangle \(CDE\), the diagonals of the kite bisect each other. Let \(CE=\frac{AC}{2}\) and \(DE = \frac{BD}{2}\). So \(CE=\frac{18}{2}=9\) and \(DE=\frac{24}{2}=12\).
By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = CE\), \(b = DE\), and \(c = CD\).
\[CD=\sqrt{CE^{2}+DE^{2}}\]
\[CD=\sqrt{9^{2}+12^{2}}=\sqrt{81 + 144}=\sqrt{225}\]

Step3: Calculate the value of \(CD\)

\(\sqrt{225}=15\)

Answer:

15