Preparing for the Regents Examination Geometry, AK

12 7 √ 2
13 4
14 5 √ 3
15 x 6 √ 3 , y 12, z 6 √ 2
16 a 6 by 6 √ 3
b 12 12 √ 3
c 36 √ 3
17 9 √ 2
18 46
19 AB 16 √ 3 , AC 24, DC 8, DB 16
20 2.28
21 a 8
b 2
12-10 Perimeters, Areas,
and Volumes of Similar
Figures (Polygons and
Solids)
(pages 336–337)
1 (1)1 : 3
2 (3) 3 : 5
3 (1) 28
4 a 9 : 1 b 16 : 81 c 81 : 4
d 25 : 1 e 2 : 3
5 a 2 : 3 b 6 : 5 c 1 : 7
d 2 : 5
6 1 : 9
7 343
8 13.5
9 25 : 1
10 539 ft
e 9 : 11
2
11 1 : 25
12 27 : 64
13 48
14 27 ft 3
15 27.7 in.
16 506.25 kg
17 a 1 : 9 b 1 : 3
18 a Yes b 2 : 3 c 4 : 9 d 8 : 27
e Ratio of surface areas: 312 _
4
702 _
9
Ratio of volumes: 360 _ 8
1,215 _
27
19 72
20 a 2.4 b 27 : 125
78 Chapter 12: Ratios, Proportion, and Similiarity
Chapter Review (pages 338–341)
1 (1) 4 : 25
2 (4) 5 : 14
3 (3) 15
4 (2) x a _
a
5 (3) √ 3
6 (4) 64 pounds
7 a 6 b 6 c an _
8 a 5 : 6 b 2 : 9
m
c n : m d c : (a b)
e p : (m n) f (m n) : (a b)
g (n b) : (a m)
9 a 6 b 8a c 10 _
10 30
11 11.25
12 6 : 35
13 6
14 6
15 14
3
16
ac bc _
a
17
8 _ 5
8 x _ 8
, EC
x 4 _ , AC
3 20 _
3
18 a 3
19 54
b Expansion
20 102
21 Yes, the ratio of similitude is 3 _ .
2
22 Yes, the ratio of similitude is 1 _
23 mQ 125, PQ 6 _ , QR 2
5
24 2
25 13
26 BD 12, AB 4 √ 13 , BC 6 √ 13
27 20, 21, 29
28 a 5 √ 2
b 50
29 34
30 x 40 √ 3 , y 80
31 x 8 √ 3 , y 8
32 x 6 √ 3 , y 9
33 √ 2
34 126
35 75 ft 2
36 8 _
27
37 80 in. 3
38 81
39 45
40 18
41 72 √ 3 in. 2
42 Area 60, perimeter 24 10 √ 2
2 .