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 is bisected by the other. Let the intersection of the diagonals be point E. In kite ABCD, diagonal AC is bisected by diagonal BD at E. So, AE = EC = 18 and BE = ED = 24.

Step2: Apply Pythagorean theorem

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

Step3: Calculate the squares

First, calculate \(18^{2}=18\times18 = 324\) 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