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

Answer

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).