6th Grade Math Textbook, Fundamentals

Lesson 6-8 for exercise sets. &KDSWHU 

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1.A tower that is 75 feet high casts a

shadow. At the same time, a 250-ft-high

building next to the tower casts a shadow

that is 25 feet long. How long is the

shadow cast by the tower?

3.Similar triangular sails are raised on two

sailboats. If the smaller sail is 1.5 m wide

and 4.5 m tall and the larger sail is 6 m

wide, how tall is the larger sail?

5.Discuss and Write Give some examples of when you would use indirect measurement.

Triangle DELand triangle JKLare similar right

triangles. What is the distance of the track span across

the gorge if KLis 8 meters?

 Set up a proportion.

Let xthe length of DE.

Solve: 

8 x17 • 32 Cross multiply.



x 68

So the length of the track over the gorge is 68 meters.

Divide both sides by 8

to isolate x.

544

8

8 x

8

32

8

x

17

EL

KL

DE

JK

2

2.A lamppost is 6.5 meters high. Next to

it, a 1.2-meter-high mailbox casts a

shadow 3.6 meters long. How long is

the shadow of the lamppost?

4.How long is the shadow cast by a

50.5-meter-tall building if, at the same

time, the shadow cast by a 1.5-meter-tall

passerby is 3 meters long?

Check:

68(8) 17(32)

544  544

?

32

8

(^68) ?
17
Triangle RTVis similar to triangle STU. Side SThas a
length of 4.5 cm, side TUhas a length of 6.5 cm, and
side TVhas a length of 13 cm. What is the length of
side RT?
 Set up a proportion.
Let xthe length of RT.
Solve: 
4.5 • 13 6.5x Cross multiply.
 Divide both sides by 6.5 to isolate x.
9 x
So the length of side RTis 9 cm.
6.5x
6.5
58.5
6.5
6.5
13
4.5
x
TU
TV
ST
RT
3
Check:
4.5(13) 9(6.5)
58.5 58.5 Tr u e
?

6.5
13
4.5
9
?

V
T
U
S R
FP
FP
FP
D
E
L
32 m 17 m
J
K