Final answer:
To find the length of the corresponding side of the larger triangle, we compare the areas of the two triangles using the scale factor. The length of the corresponding side can be found by multiplying the length of the smaller triangle's side by the square root of the ratio of the areas.
Step-by-step explanation:
To find the length of the corresponding side of the larger triangle, we need to find the scale factor by comparing the areas of the two triangles. The area of the smaller triangle is 24 square cm and the area of the larger triangle is 54 square cm. The ratio of the areas is 54/24 = 9/4. Since the side length of the smaller triangle is 6 cm, we can find the length of the corresponding side of the larger triangle by multiplying 6 cm by the square root of the ratio: sqrt(9/4) = 3/2.