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 2nd longest side on quadrilateral EFGH?

Answer 1

The two quadrilaterals are given similar .

In any similar figure sides are in proportion.The second largest side of quadrilateral ABCD is 16 ft .Let the second longest side of quadrilateral EFGH be x ft. These sides will be in proportion to each other .

The second shortest side of quadrilateral EFGH that is GF will be proportional to the third longest side of quadrilateral ABCD that is BC

We can form a proportion with the proportional sides:

$\frac{16}{x} =\frac{12}{18}$

To solve for x we cross multiply

12x=(16)(18)

12x=288

Dividing both sides by 12 we get

x=24.

The second longest side of quadrilateral EFGH is 24 ft.