Final answer:
To determine the lengths of the diagonals of the kite, we need more information because the given equation has two variables. The area formula for a kite is 0.5 times the product of its diagonals.
Step-by-step explanation:
The area of a kite is given by the formula ½ times the product of its diagonals. If the area is 24 cm² and the lengths of the diagonals are (x-a) cm and (x+4) cm respectively, we can set up the following equation based on the area formula for kites:
½ * ((x - a) * (x + 4)) = 24
Simplifying the equation gives:
(x - a)(x + 4) = 48