Final answer:
To find the length of the shortest side of the larger triangle, we can use the ratio of the areas of the two similar triangles. The scale factor between the triangles can be determined by taking the square root of the ratio of their side lengths squared. Setting up a proportion, we can solve for the length of the shortest side of the larger triangle, which is 14.
Step-by-step explanation:
To find the length of the shortest side of the larger triangle, we need to determine the scale factor between the two triangles. The ratio of the areas of the triangles is given as 9:49, which means the ratio of their side lengths squared is also 9:49. Since the ratio is squared, we can take the square root to find the ratio of the side lengths, which is 3:7.
Since the shortest side of the smaller triangle measures 6, we can set up the following proportion:
3/7 = 6/x
Cross-multiplying, we get 3x = 42, and dividing both sides by 3, we find that x = 14. Therefore, the length of the shortest side of the larger triangle is 14. So, the answer is D) 56.