6th Grade Math Textbook, Progress

Write a proportion. Then solve.

1. An 8-foot electricity pole casts a
   12-foot shadow. At the same time,
   Ruth Ann casts a 9-foot shadow.
   How tall is Ruth Ann?


2. Similar triangular sails are raised
   on two sailboats. If the larger sail is
   5 m wide and 10 m high and the
   smaller sail is 6 m high, how wide
   is the smaller sail?


3. A 6-ft-tall person casts a shadow 15 ft
   long. At the same time, a nearby tower
   casts a shadow 100 ft long. Find the
   height of the tower.


4. A mailbox that is 1 meter tall casts
   a shadow 4 meters long, while a
   lamppost casts a shadow 24 meters
   long. How tall is the lamppost?


5. A triangular sail has sides of 10 ft,
   24 ft, and 26 ft. If the shortest side of
   a similar sail measures 6 ft, what is
   the measure of its longest side?


6. A surveyor determines the width of a
   river by setting up similar triangles as
   shown in the given figure.
   
   AEC
   
   BEDwith AC
   89.5 ft,
   CE
   20 ft, and DE
   80 ft. What is
   the width of the river BD?
   4. What is the height of a vertical pole
   that casts a shadow 8 ft long at the
   same time that a 12-ft-high vertical
   pole casts a shadow 3 ft long?
   6. A lamppost is 6.5 meters high. Next
   to it, a 1.2-meter-high mailbox casts
   a shadow 4.8 meters long. How long
   is the shadow of the lamppost?
   8. The heights of two signal poles are
   20 feet and 30 feet, respectively. If the
   shorter pole casts a shadow of 8 feet,
   how long is the taller pole’s shadow?

10.On the school softball team, there

are 3 boys for every 4 girls. If the

team has 21 members, how may

boys does it have? how many girls?

11.A football team has 6 players who

play offense for every 5 who play

defense. There are 33 players on the

team. How many players play offense?

how many play defense?

F

S

w

6 m

B

F

10 m

XR5 m

8 ft

12 ft 9 ft

h

A

E

C

DB

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