Question

Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 24 feet, 16 feet, and 12 feet long. If the two shortest sides of quadrilateral EFGH are 9 feet long and 18 feet long, how long is the 4th side on quadrilateral ABCD?

Answer 1

Refer to the figure shown below.

Quadrilaterals ABCD and EFGH are similar.

The shortest side (the 4th side) of quadrilateral ABCD is AD = x.
The three longest sides are
AB = 24, BC = 16 and CD = 12 feet.

The corresponding shortest sides of quadrilateral EFGH are
EH = 9, and GH = 18 feet.

Because the two quadrilaterals are similar, therefore

`(AB)/(EF)= (AD)/(EH) \\ \\ (x)/(9) = (12)/(18) \\ \\ x= (9 * 12)/(18) =6`

Answer: The length of the 4th side of quad ABCD is 6 feet.