two triangles used in an art project are similar. the sides of the similar 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
To find the lengths of the sides of the larger triangle, we need to set up a proportion between the corresponding sides of the two similar triangles.
Let x be the length of the shortest side of the larger triangle.
Using the proportion of corresponding sides:
6 / x = 12 / 7
Cross multiplying:
6 * 7 = 12 * x
42 = 12x
x = 42 / 12
x = 3.5
Therefore, the length of the shortest side of the larger triangle is 3.5 inches.