The sides of a triangle are 6: 7: 8. Find the perimeter of a similar triangle whose average length is 24 cm.

Let’s find the sides of the triangle. Let a, c – unknowns, the third = 24 cm. From the similarity: a: 24: c = 6: 7: 8. Hence a: 24 = 6: 7 => a = 6 * 24: 7 = 144/7, 24: c = 7: 8 => c = 192/7. Knowing the 3 sides of the triangle, we can find its perimeter. Perimeter is the sum of the lengths of all sides. Perimeter = 24 + 144/7 + 192/7 = 72 (cm).
Answer: 72 cm.