The lengths of the sides of a triangle are 3,5, and 7 inches. How many inches long is the shortest side of a similar triangle that has a perimeter of 75 inches?

F.10
G.12
H.14
H.15
k.22

given triangle has perimeter 3+5+7 = 15

75 is 5*15, so all the sides have to be scaled up by 5. The smallest would thus be 5*3 = 15

(I)

To find the length of the shortest side of a similar triangle, we need to determine the scale factor between the two triangles. In similar triangles, the ratio of corresponding side lengths is always the same.

Let's start by finding the scale factor. The perimeter of the original triangle is 3 + 5 + 7 = 15 inches. The perimeter of the similar triangle is given as 75 inches.

To find the scale factor, we divide the perimeter of the similar triangle by the perimeter of the original triangle:

Scale factor = Perimeter of Similar Triangle / Perimeter of Original Triangle
= 75 inches / 15 inches
= 5

Now, we can multiply each side length of the original triangle by the scale factor to find the corresponding side lengths of the similar triangle.

The shortest side length of the original triangle is 3 inches. Multiplying it by the scale factor of 5, we get:

Shortest side length of similar triangle = 3 inches * 5
= 15 inches

Therefore, the shortest side of the similar triangle is 15 inches. So, the correct answer is:

H. 15