Ratios and Proportions
Simplify the ratio.
1. 1 oz : 2 qt
2. 4 seconds : 1 year
Find the ratio of AB to AC in simplest form.
3.
4.
The perimeter and the ratio of the length to the width of a rectangle are given. Find the length and width
of the rectangle.
5. Perimeter: 132 cm
6. Perimeter: 280 ft
l : w = 7 :4
l:w = ll:9
The measures of the angles of a triangle are in the extended ratio given. Find the measures of the angles
of the triangle.
7. 2:5:5
8. 3:7:10
Solve the proportion.
9. 5  20
8 y
10.
3
1

x x6
Find the geometric mean of the two numbers.
12. 2 and 8
13. 7 and 14
Solve the proportion.
15. 12  x
x 4
16.
y  2 2y  3

2
5
11.
3
2

m 5 m 1
14. 10 and 12
17.
8
z2

z2
4
In Exercises 18-19, the ratio of two side lengths for the triangle is given. Solve for the variable.
18. AB : AC i s 2 : 1.
19. AB : AC is 15 : 8.
20. 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.
21. Currency Exchange You and a friend win a free trip to Europe. The plane trip includes a layover in
Canada before continuing service to Europe. At the time of your trip, the currency exchange rates are 1
U.S. dollar per 1.14 Canada dollar and 1 U.S. dollar per 0.84 Euros.
a. During the layover, you purchase a book that costs $20 in Canadian currency. How much does the
book cost in U.S. dollars?
b. Once you arrive in Europe, you exchange $80 in U.S. currency. How many Euros do you get for that
amount?
Complete the statement.
22.
If
7
10

x
y
, then
10
7

?
?
.
23. If
AB AG

.
In the diagram, AB  AG and
AC AF
CD FE
Find the unknown length.
12.
13.
Find AB
Find GF
6
x

24
y
, Then
6
24

?
.
?
PQ WV QR VU
PW QV

,

and

QR VU RS UT
QV
ST
Find the unknown length.
In the diagram,
14. Find UT.
15. Find QV.