Download Geometry: Review 6.1

Geometry: Review 6.1-6.2
Name_______________________________________________
Simplify the ratio.
1. $12:$16
2.
6 cm
14 cm
3. 3 gallons: 10 quarts
Find the ratio of the width to the length of the rectangle. Then simplify the ratio.
4.
5.
Use the number line to find the ratio of the distances.
6.
BF
CD
7. BE
AD
8. Perimeter The perimeter of a rectangle is 56 inches. The ratio of the length to the width is 6 : 1. Find the
length and the width.
9. Area The area of a rectangle is 525 square centimeters. The ratio of the length to the width is 7 : 3. Find the
length and the width.
The measures of the angles of a triangle are in the extended ratio given. Find the measures of the angles of
the triangle.
10. 1:7:10
11. 5 : 6 : 7
1 2 . 7:14:15
Solve the proportion.
4
x

13.
5 15
14.
z  2 27

4
12
Find the geometric mean of the two numbers.
16. 2 and 8
17. 7 and 14
15.
3
2

m 5 m  1
18. 10 and 12
Let x = 6, y = 3, and z = 2. Write the ratio in simplest form.
19. 2 x  y
20. z  2 y
3
2x  4
21. Area The perimeter of the rectangular front lawn of the library is 192 feet. The ratio of the length to the
width is 5 :3. Find the area of the lawn.
Copy and complete the statement.
6
?
6 5


22. If
, then
5
?.
x y
24. If
x

4
x
x
y
, then 

y
12 2
6
9
x
11


25. If
, then
2 y
2
23. If
7

, then x 4  ?
y
4
?
Decide whether the statement is true or false.
3
y
y
3
x
8
x
8



26. If
, then
.
27. If  , then
.
x
x
8
y 3
8
y 3
29. If
x

y
8
3
, then
x
8

y
3
.
30. If
x
y

8
3
, then
?
?.
?
?.
x
28. If

y
FD
FE

CD
BE
,
find BE
3
, then
8

3
y
x 2y
x
8
x 8 y 3
. 31. If 
, then

y
y 3
8
3
Use the diagram and the given information to find the unknown length.
AB
AE
AE , find BC.

32. Given AB
33. Given
find BC

BC
ED ,
,
BC
ED
34. Given
x
8
35. Given
AB
BC

FE
ED ,
find AC.
.
 14
3
36. Map Scale On a map, two neighboring towns are 2.4 inches apart. The actual straight line distance between
the two towns is 36 miles. What is the scale of the map?
37. Sales Tax You plan on purchasing a new $25,000 vehicle. Recently, a friend bought a $22,500 vehicle and
paid an additional $1575 in sales tax. Assuming the same sales tax rate applies, how much should you expect to
pay in sales tax?
Scale Model You purchase a scale model of a train. The model states that the scale is 1 inch: 5.4 feet.
38. If the model is 10 inches long, how long is the actual train?
39. The actual height of the train is 13.5 feet, how tall is the model?
Mexican Pesos In November, 2005, the exchange rate of Mexican pesos to U.S. dollars was 10.77 to 1. While
on vacation, you paid 205 pesos for a sombrero at a gift shop.
40. What was the price of the sombrero in U.S. dollars?
41. If the exchange rate were 9.24 Mexican pesos to 1 U.S. dollar, what would have the cost been in U.S.
dollars?
Canadian Dollars In November, 2005, the exchange rate of Canadian dollars to U.S. dollars was 1 to 0.85. A
Canadian citizen paid $12.28 in U.S. dollars for lunch while visiting New York City.
42. What was the price of the lunch in Canadian dollars?
43. If the exchange rate were 1.28 Canadian dollars to 1 U.S. dollar, what would have the cost been in
Canadian dollars?