By exploiting the similarity of triangles and the property that corresponding sides are in proportion, we establish the ratio x/2.8 = 3/2.4 = 4.5/y. Solving for x, we determine x = 3.5.
The correct answer is (A) 3.5.
To find the value of x in the larger triangle with sides x, 3, 4.5, and the smaller triangle with sides 2.8, 2.4, y, we utilize the property of similar triangles.
Two triangles are similar if their corresponding angles are equal, and the ratios of their corresponding sides are in proportion. In this case, we set up a proportion using the corresponding sides:
x/2.8 = 3/2.4 = 4.5/y
Solving the first ratio, we find x = (3 * 2.8)/2.4 = 3.5.
So, the correct answer is (A) 3.5.