Final answer:
The lengths of the parallel sides of the trapezium are found to be 39 cm and 26 cm, using the formula for the area of the trapezium and the provided ratio of the sides.
Step-by-step explanation:
The question asks for the length of the parallel sides of a trapezium with a known area and the ratio of the lengths of the parallel sides. To find the lengths of the parallel sides, we can use the formula for the area of a trapezium, which is (1/2) × (sum of parallel sides) × (distance between them). Given the area of the trapezium is 325 cm² and the distance between the parallel sides is 10 cm, we set up an equation:
(1/2) × (a + b) × 10 = 325
Since the ratio of the lengths of the parallel sides a and b is 3:2, we can write b = (2/3)a. Substituting b in the area equation we get:
(1/2) × (a + (2/3)a) × 10 = 325
(1/2) × (5/3)a × 10 = 325
a = (325 × 2) / (10 × (5/3))
a = 39 cm
Now we find b using the ratio b = (2/3)a:
b = (2/3) × 39 = 26 cm
Therefore, the lengths of the parallel sides are a = 39 cm and b = 26 cm.