Final answer:
The perimeter of the larger triangle, which has side lengths twice that of the smaller triangle with sides of 3 in, 4 in, and 12 in, is 36 in (option C).
Step-by-step explanation:
The correct answer is option C, 36 in. To find the perimeter of the larger triangle, we first need to determine the relationship between the smaller and larger triangles. Given that the side lengths of the smaller triangle are 3 in, 4 in, and 12 in, and that the corresponding sides of the larger triangle are twice the length, we can calculate the side lengths of the larger triangle by multiplying each by 2. Therefore, the sides of the larger triangle are 6 in, 8 in, and 24 in. The perimeter of the larger triangle is found by adding these side lengths together: 6 in + 8 in + 24 in, which equals 36 in.
To find the perimeter of the larger triangle, we need to determine the scale factor between the two triangles. Since the vertical sides of each triangle correspond, we can compare the lengths of the vertical sides. The vertical side of the smaller triangle is 3 in, and the corresponding side of the larger triangle would be 2 times that length, which is 6 in.
The perimeter of a triangle is the sum of its three sides. In the larger triangle, the side lengths are 6 in, 12 in (corresponding to the horizontal side of the smaller triangle), and 8 in (corresponding to the diagonal side of the smaller triangle). Therefore, the perimeter is 6 + 12 + 8 = 26 inches.