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 property of kite

In a kite, the diagonals are perpendicular and one diagonal bisects the other. Let the intersection of the diagonals be point E. Here, the diagonals AC and BD are perpendicular, and assume AC is bisected by BD. 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 \(a = 18\), \(b = 24\), and we want to find the hypotenuse CD. So, \(CD=\sqrt{18^{2}+24^{2}}\).

Step3: Calculate the value

First, calculate \(18^{2}=324\) and \(24^{2}=576\). Then \(18^{2}+24^{2}=324 + 576=900\). And \(\sqrt{900}=30\).

Answer:

30