The lengths of the sides of a triangle are 4in.,14 in., and 16 in.If the longest side of a similar triangle measures 40 in., what is the length of the shortest side of this new triangle?

40/16 = x/4

Solve for x.

To find the length of the shortest side of the new triangle, we can use a proportion based on the similarity of the two triangles.

The two triangles are similar because their corresponding angles have the same measures. In similar triangles, the ratio of corresponding sides is equal.

Let's set up a proportion using the given lengths of the sides:

(Shortest side of the new triangle) / (Longest side of the new triangle) = (Shortest side of the original triangle) / (Longest side of the original triangle)

x / 40 = 4 / 16

To solve for x, we can cross-multiply and then divide:

16x = 4 * 40

16x = 160

x = 160 / 16

x = 10

Therefore, the length of the shortest side of the new triangle is 10 inches.