Final answer:
To solve for the lengths of the kite diagonals, we utilize the area formula for a kite and the given condition that one diagonal is twice the length of the other, arriving at a solution where the diagonals measure 4 cm and 8 cm.
Step-by-step explanation:
To find the length of each diagonal of the kite, given that one diagonal is twice the length of the other and the area of the kite is 16 cm2, we can use the formula for the area of a kite. The area (A) of a kite is given by the product of its diagonals (d1 and d2) divided by 2, as follows: A = (d1 * d2)/2.
If we let d1 be the length of the shorter diagonal, d2 will be twice that, so d2 = 2 * d1. Substituting the given area into the formula, we get: 16 = (d1 * 2 * d1)/2.
Solving this equation for d1, we get d1^2 = 16, so d1 = 4 cm. Accordingly, d2 = 2 * d1 = 2 * 4 cm = 8 cm.
Therefore, the lengths of the diagonals are 4 cm and 8 cm.