Question

what is the length of the sides of kite abcd? ab = 20, cd = 15 ab = 15, cd = 20 ab = 8, cd = 18 ab = 24, cd = 25

Explanation:

Step1: Find length of AB

Use the Pythagorean theorem in right - triangle formed by half of AC and the line from B to the mid - point of AC. The half of AC is 12, and the height from B to AC is 9.
Let the length of AB be $l_{AB}$. By the Pythagorean theorem $l_{AB}=\sqrt{12^{2}+9^{2}}=\sqrt{144 + 81}=\sqrt{225}=15$.

Step2: Find length of CD

Use the Pythagorean theorem in right - triangle formed by half of AC and the line from D to the mid - point of AC. The half of AC is 12, and the height from D to AC is 16.
Let the length of CD be $l_{CD}$. By the Pythagorean theorem $l_{CD}=\sqrt{12^{2}+16^{2}}=\sqrt{144+256}=\sqrt{400}=20$.

Answer:

AB = 15, CD = 20