Final answer:
In a kite, the intersecting diagonals form right angles. By applying the Pythagorean Theorem, we can find the length of KL. The length of KL in this kite is 8.
Step-by-step explanation:
In a kite, the diagonals intersect at a right angle. Therefore, if we draw the diagonal JL, it will intersect the diagonal KM at a right angle.
Given that JL = 10 and KN = 12, we can use the Pythagorean Theorem to find KL.
Let x represent KL. According to the Pythagorean Theorem, JL2 = JK2 + KL2. Plugging in the values, we have 102 = 122 + x2. Solving for x, we find KL = 8.