The table shows the number of bases stolen by a baseball player during several games over a season. A 2-column table with 5 rows. Column 1 is labeled Games of the season with entries 2, 3, 4, 7, 10. Column 2 is labeled Based stolen by Williams with entries 3, 1, 3, a, 2. In the seventh game of the season, Williams stole the same number of bases as in the third game of the season. What is the value of a? a =

look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3