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 and one diagonal bisects the other. Let the intersection of the diagonals be point E. Here, AC and BD are diagonals, AC = 18 + 18=36, BD = 24 + 24 = 48, and they are perpendicular.

Step2: Use Pythagorean theorem

In right - triangle CDE, CE = 18 and DE = 24. According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 18\), \(b = 24\), and \(c\) is the length of CD. So \(CD=\sqrt{18^{2}+24^{2}}\).

Step3: Calculate \(18^{2}\) and \(24^{2}\)

\(18^{2}=18\times18 = 324\) and \(24^{2}=24\times24=576\). Then \(18^{2}+24^{2}=324 + 576=900\).

Step4: Find the square - root

\(CD=\sqrt{900}=30\).

Answer:

30