A parallelogram-shaped signboard has adjacent sides of 24 cm and 18 cm. The perpendicular distance between the two sides of length 24 cm is 15 cm. What is the perpendicular distance, in cm, between the two sides of length 18 cm?

A parallelogram has one area, whichever pair of sides you call the base: area = $24\times 15=360$ sq cm, so with the 18 cm side as base the height must satisfy 18 $xh=360$, giving $h=20$ cm. The shorter side needs the taller height. The trap $11.25=18\times 15/24$ divides by the wrong side and makes the shorter base go with the shorter height; 15 assumes both heights are the same, which happens only in a rhombus; 7.5 halves the given height, borrowing the triangle's 1/2 into a formula that has none.