Question

Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 20 feet, 18 feet, and 14 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 5 feet long, how long is the 2nd longest side on quadrilateral EFGH?

Answer 1

check the picture below.

since we know that the quadrilaterals are similar, we can simply use proportions.

we can use corresponding sides GH and CD to get the ratio of both figures

$\bf \cfrac{small~figure}{large~figure}\qquad \cfrac{GH}{CD}\implies \cfrac{12}{30}\implies \cfrac{2}{5} \\\\\\ \textit{so the figures are in a ratio of }2:5\qquad therefore \\\\\\ \cfrac{small~figure}{large~figure}\qquad \cfrac{FG}{BC}=\cfrac{2}{5}\implies \cfrac{FG}{40}=\cfrac{2}{5}\\\\\\ FG=\cfrac{40\cdot 2}{5}\implies FG=16$