Download Geometry

Name__________________________________________ Date_________________ Period______
Mr. Gmerek
Geometry
Problem Set 6.2
1.
The geometric mean of two positive numbers a and b is a number x that satisfies
a.
a x
 .
x b
Solve this for x.
2.
Find the geometric mean of 8 and 18.
3.
In the picture on the right…
a. What is the ratio of angle A to angle B?
b.
What is the ratio of angle C to angle A?
c.
Find the value of x. Then find the measure of each angle.
4.
The perimeter of the following isosceles triangle is 56 cm. The ratio of LM:MN is 5:4. Find the lengths of all the
sides.
5.
The perimeter of rectangle ABCD is 60cm. The ratio of AB:BC is 3:2. Find the length and the width of the
rectangle.
6.
The measures of the three angles in a triangle are in extended ratio of 3:4:8. Find the measures of all the angles.
7.
The area of a rectangle is 192m². The ratio of the width to the length is 1:3. Find the length and the width.
8.
The official height-to-width ratio of the United States flag is 1:1.9. If a United States flag is 6 feet high, how
wide is it?
9.
The ratios of the side lengths of ΔQRS to the corresponding sides of ΔVTU is 3:2. Find the lengths of all of the
missing sides. If necessary, leave answers as radicals in simplest form.
10. The perimeter of a rectangle is 84 feet. The ratio of the width to the length is 2:5. Find the width and the
length of the rectangle.
11. The area of a rectangle is 108 cm². The ratio of the length to the width is 4:3. Find the length and the width of
the rectangle.
Name__________________________________________ Date_________________ Period______
12. The ratios of the side lengths of ΔPQR to the corresponding side lengths of ΔSTU are 1:3. Find all of the missing
lengths.
13. In the diagram on the right,
AB AC
=
. Find the length of BD.
BD CE
14. Use the diagram below to answer a and b.
a.
MQ LQ
=
. Find the length of LQ.
MN
LP
b.
LM MQ
. Find PN.
=
PN NQ
15. The ratio of BC:AC:AB is 3:4:5. Find the lengths of the unknown sides.
16. The geometric mean of two numbers is 16. One of the numbers is 4. Find the other number.
17. Find the geometric mean of each pair of numbers.
d. 3 and 27
e.
7 and 28
f.
5 and 15
18. Given the triangle below, the ratio of angle A to angle B is 1:4. Find the measures of all three angles in the
triangle.
19. In the picture on the right, the ratio of SU:ST is 4:1.
Find the value of m and the lengths of these two sides.
20. Given:
VW VX
=
. Find VX.
WY XZ
21. Given:
QU RV
. Find SU.
=
QS RT