Final answer:
To find the lengths of the parallel sides of the trapezium, we can set up the equation for the area of a trapezium and solve for the unknowns. The lengths of the parallel sides are 6.5 cm and 11.5 cm.
The correct answer is none of all.
Step-by-step explanation:
To find the lengths of the parallel sides of the trapezium, we can use the formula for the area of a trapezium: A = 1/2(a + b)h, where a and b are the lengths of the parallel sides and h is the distance between them.
In this case, we are given that the area of the trapezium is 390 and the distance between the parallel sides is 12 times the length of the parallel sides.
Let x be the length of the shorter side. The longer side is then x + 5.
Using the given information, we can set up the equation:
390 = 1/2(x + x + 5)(12x)
Simplifying and solving for x, we get:
390 = 1/2(2x + 5)(12x)
780 = (2x + 5)(12x)
780 = 24x^2 + 60x
Dividing both sides by 12, we get:
65 = 2x^2 + 5x
Rearranging the equation, we get:
2x^2 + 5x - 65 = 0
Factoring the equation, we get:
(2x - 13)(x + 5) = 0
Solving for x, we get x = 13/2 or x = -5. Since the length of a side cannot be negative, we can discard x = -5.
Therefore, the lengths of the parallel sides are x = 13/2 and x + 5 = 13/2 + 5 = 23/2.
Converting the lengths to centimeters, we get the lengths of the parallel sides as: 6.5 cm and 11.5 cm.