Question

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: Use Pythagorean theorem for AB

In right - triangle formed by half of the diagonals for side AB. Sides of right - triangle are 9 and 12. By Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 9\), \(b = 12\), then \(AB=\sqrt{9^{2}+12^{2}}=\sqrt{81 + 144}=\sqrt{225}=15\).

Step2: Use Pythagorean theorem for CD

In right - triangle formed by half of the diagonals for side CD. Sides of right - triangle are 12 and 16. By Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 12\), \(b = 16\), then \(CD=\sqrt{12^{2}+16^{2}}=\sqrt{144+256}=\sqrt{400}=20\).

Answer:

AB = 15; CD = 20