Question

calculating side lengths of a kite
what is the length of the sides of kite abcd?
ab = 20; cd = 15
ab = 15; cd = 20
ab = 9; cd = 16
ab = 24; cd = 25

Explanation:

Step1: Calculate the length of \(AB\)

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) in \(\triangle ABC\) (where \(a = 9\), \(b=12\)).
\(AB=\sqrt{9^{2}+12^{2}}=\sqrt{81 + 144}=\sqrt{225}=15\)

Step2: Calculate the length of \(CD\)

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) in \(\triangle ADC\) (where \(a = 16\), \(b = 12\)).
\(CD=\sqrt{16^{2}+12^{2}}=\sqrt{256+144}=\sqrt{400}=20\)

Answer:

\(AB = 15; CD = 20\) (the second option)