Two similar triangles have corresponding medians in the ratio 5 : 3. The perimeter of the larger triangle is 40 cm. What is the perimeter of the smaller one?

In similar triangles every pair of corresponding LENGTHS — sides, medians, altitudes, angle bisectors and perimeters alike — shares the same ratio, here 5 : 3. So the smaller perimeter = $40\times 3/5=24$ cm. Squaring the ratio, as one correctly does for areas, gives the trap $40\times 9/25=14.4$ cm; the square rule never applies to perimeters. Turning the ratio the wrong way up gives 66.7 cm, and doing both gives 111.1 cm.