Geometry Big Ideas Math Answers

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Chapter eight

Affiliate 8 Maintaining Mathematical Profi ciency (p. 415)

i. v

—

3 =

5 ⋅ 7

—

iii ⋅ 7 =

35

—

21

5

—

3 and

35

—

21 form a proportion.

2. 9 ÷ 3

—

24 ÷ 3 =

3

—

8

24 ÷ 8

—

64 ÷ eight =

3

—

8

9

—

24 and

24

—

64 form a proportion.

3. 8 ÷ 8

—

56 ÷ eight =

1

—

7

half-dozen ÷ 2

—

28 ÷ ii = 3

—

14

eight

—

56 and 6

—

28 do non form a proportion.

4. 18 ÷ 2

—

four ÷ 2 =

9

—

2

27 ÷ 9

—

9 ÷ ix =

3

—

1 = iii

xviii

—

4 and

27

—

9 do not class a proportion.

5. 15 ÷ 3

—

21 ÷ 3 =

5

—

7 6.

26 ÷ 2

—

eight ÷ 2 =

13

—

4

55 ÷ 11

—

77 ÷ xi =

5

—

7 39 ÷ iii

—

12 ÷ 3 =

13

—

iv

15

—

21 and

55

—

77 grade a

26

—

eight and

39

—

12 form a

proportion. proportion.

vii. CP′

—

CP = six

—

14 =

3

—

vii 8.

CP′

—

CP =

24

—

9 =

8

—

iii

The scale gene is The calibration factor is

k =

3

—

7 . chiliad =

8

—

3 .

9. M′K′

—

MK =

28

—

14 = two

The scale factor is grand = 2.

x. yes; All of the ratios are equivalent by the Transitive Property

of Equality.

Chapter viii Mathematical Practices (p. 416)

ane. a. yard = 2

P = 2 + v + 6 + iii = sixteen centimeters

kP = 2 ⋅ 16 = 32 centimeters

A =

one

—

2

⋅ 3 ⋅ (two + 6)

=

1

—

2

⋅ 3 ⋅ (viii)

= 3 ⋅ (4)

= 12 square centimeters

k 2 A = 2two ⋅ 12 = 4 ⋅ 12 = 48 square centimeters

b. k = 3

P = two + 5 + 6 + iii = 16 centimeters

kP = iii ⋅ sixteen = 48 centimeters

A =

1

—

2

⋅ 3 ⋅ (2 + 6)

=

i

—

2

⋅ 3 ⋅ (8)

= three ⋅ (4) = 12 square centimeters

k ii A = iiitwo ⋅ 12 = ix ⋅ 12 = 108 square centimeters

c. k = four

P = two + 5 + six + 3 = 16 centimeters

kP = 4 ⋅ 16 = 64 centimeters

A =

1

—

2

⋅ 3 ⋅ (2 + half-dozen)

=

1

—

2

⋅ 3 ⋅ (8)

= 3 ⋅ (4) = 12 square centimeters

1000twoA = 4two ⋅ 12 = 16 ⋅ 12 = 192 square centimeters

two. a. thousand = ii

P = ii + five + 2 + 5 = 14 feet

kP = 2 ⋅ 14 = 28 feet

A = 2 ⋅ four = eight square feet

1000 two A = 2two ⋅ eight = 4 ⋅ viii = 32 square feet

b. k = three

P = 2 + v + 2 + five = xiv feet

kP = iii ⋅ 14 = 42 feet

A = 2 ⋅ 4 = 8 square feet

thousand 2 A = iiitwo ⋅ 8 = 9 ⋅ 8 = 72 square feet

c. k =

1

—

2

P = ii + 5 + 2 + v = 14 anxiety

kP =

1

—

2

⋅ 14 = 7 anxiety

A = two ⋅ 4 = 8 square feet

thou ii A =

(

1

—

2

)

2 ⋅ 8 =

1

—

4

⋅ 8 = 2 foursquare anxiety

3. Surface area = ii ⋅ tiptop ⋅ width + ii ⋅ top ⋅ length

+ 2 ⋅ length ⋅ width

Volume of a rectangular prism = length ⋅ width ⋅ height

a. thou = two

Due south = ii ⋅ 5 ⋅ 3 + 2 ⋅ 5 ⋅ iv + ii ⋅ 3 ⋅ 4

= 30 + 40 + 24 = 94 square inches

k two S = 4 ⋅ 94 = 376 square inches

V = 3 ⋅ 4 ⋅ 5 = 60 cubic inches

k 3 V = 23 ⋅ 60 = 8 ⋅ 60 = 480 cubic inches

b. k = 3

S = 2 ⋅ 5 ⋅ 3 + ii ⋅ 5 ⋅ 4 + 2 ⋅ 3 ⋅ iv

= 30 + 40 + 24 = 94 square inches

k 2 Due south = 9 ⋅ 94 = 846 square inches

V = 3 ⋅ four ⋅ v = threescore cubic inches

thousand 3 V = iiithree ⋅ 60 = 27 ⋅ 60 = 1620 cubic inches

Geometry Big Ideas Math Answers,

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