Question

what is the length of the sides of kite abcd?
o ab = 20; cd = 15
o ab = 15; cd = 20
o ab = 9; cd = 16
o ab = 24; cd = 25

Explanation:

Step1: Apply Pythagorean theorem for AB

In right - triangle formed by half of AC and the part of the vertical line from B to AC. The two legs of the right - triangle are 12 and 9. According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 12\), \(b = 9\), and \(c=AB\). So \(AB=\sqrt{12^{2}+9^{2}}=\sqrt{144 + 81}=\sqrt{225}=15\).

Step2: Apply Pythagorean theorem for CD

In right - triangle formed by half of AC and the part of the vertical line from D to AC. The two legs of the right - triangle are 12 and 16. According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 12\), \(b = 16\), and \(c = CD\). So \(CD=\sqrt{12^{2}+16^{2}}=\sqrt{144+256}=\sqrt{400}=20\).

Answer:

AB = 15; CD = 20