Question

Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet, 40 feet, and 30 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 12 feet long, how long is the 4th side on quadrilateral ABCD? A) 18 feet B) 24 feet C)16 feet D)20 feet

Answer 1

15 feet

Explanation:

It is given that Quadrilateral ABCD is similar to Quadrilateral EFGH. This means that the corresponding sides of these two quadrilateral will be in the same proportion.

i.e.

Ratio of two corresponding sides would be the same. We are given longest three sides of ABCD and shortest two sides of EFGH. Let the 4th sides of ABCD i.e. the shortest side be x.

So, the ratio of the shortest sides of two quadrilaterals would be the same as the ratio of second shortest sides.

So,

`x:6=30:12\\\\(x)/(6)=(30)/(12)\\\\ x=(30)/(12) * 6\\\\ x = 15`

So, the 4th side on quadrilateral ABCD would be 15 feet. None of the options match with the answer.