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 4th side on quadrilateral ABCD?

Answer 1

The 4th side on quadrilateral ABCD is
`11(2)/(3)\ ft`

Explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

The corresponding sides are

ABCD EFGH

20 ft ?

18 ft ?

14 ft 6 ft

? 5 ft

The length side of 14 ft in quadrilateral ABCD is the corresponding side to the length side of 6 ft in quadrilateral EFGH

so

the scale factor from quadrilateral ABCD to quadrilateral EFGH is

`6/14=3/7`

therefore

To find the length of the 4th side on quadrilateral ABCD, divide the length of the 4th side on quadrilateral EFGH by the scale factor

so

`5/(3/7)=35/3\ ft`

convert to mixed number

`(35)/(3)\ ft=(33)/(3)+(2)/(3)=11(2)/(3)\ ft`