To find the length of the shortest side of the larger triangle, we need to find the scale factor by comparing the corresponding sides of the two triangles.
The ratio of the corresponding sides in similar triangles is equal to the scale factor. In this case, we can set up the following proportions:
Scale factor = (Perimeter of larger triangle) / (Perimeter of smaller triangle) = 75 / (6 + 7 + 12) = 75 / 25 = 3
Since the sides of the smaller triangle are 6 in, 7 in, and 12 in, the corresponding sides of the larger triangle will be 6*3 = 18 in, 7*3 = 21 in, and 12*3 = 36 in.
Therefore, the length of the shortest side of the larger triangle is 18 in.
Two triangles used in an art project are similar. The sides of the smaller triangle have lengths of 6 in, 7 in, and 12 in. The perimeter of the larger triangle is 75 in. What is the length of the shortest side of the larger triangle?
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