year 8 maths

613
Exercise 3K
1 a 9 b 25 c 144 d 2.25
e 20 f 58 g 157 h 369
2 a false b true c true d true
e false
f false
3 hypotenuse, triangle
4 a c b x c u
5 a no b no c yes
6
d yes e yes f no
g yes h no i no
a b c a 2 b 2 a 2 + b 2 c 2
3 4 5 9 16 25 25
6 8 10 36 64 100 100
8 15 17 64 225 289 289
a 2 + b 2 and c 2
b i 13 ii 20
c i 25 ii 110
7 a 3 2 + 4 2 = 5 2 b 8 2 + 15 2 = 17 2 c 9 2 + 12 2 = 15 2
d 5 2 + 12 2 = 13 2 e 9 2 + 40 2 = 41 2 f 2.5 2 + 6 2 = 6.5 2
8 a a 2 + b 2 = x 2 b a 2 + b 2 = d 2 c d 2 + h 2 = x 2
9 a no
b No, a 2 + b 2 = c 2 must be true for a right-angled triangle.
10 {(6, 8, 10), (9, 12, 15), (12, 16, 20), (15, 20, 25), (18, 24, 30),
(21, 28, 35), (24, 32, 40), (27, 36, 45), (30, 40, 50),
(33, 44, 55), (36, 48, 60), (39, 52, 65), (42, 56, 70),
(45, 60, 75), (48, 64, 80), (51, 68, 85), (54, 72, 90),
(57, 76, 95) }, {(5, 12, 13), (10, 24, 26), (15, 36, 39),
(20, 48, 52), (25, 60, 65), (30, 72, 78), (35, 84, 91) },
{ (7, 24, 25), (14, 48, 50), (21, 72, 75) }, {(8, 15, 17),
(16, 30, 34), (24, 45, 51), (32, 60, 68), (40, 75, 85) },
{(9, 40, 41), (18, 80, 82) } , { (11, 60, 61) }, { (20, 21, 29),
(40, 42, 58), (60, 63, 87) }. { (12, 35, 37), (24, 70, 74) },
{ (28, 45, 53) }, { (33, 56, 65) }, { (16, 63, 65) }, { (48, 55, 73) },
{ (13, 84, 85) }, { (36, 77, 85) }, { (39, 80, 89) }, { (65, 72, 97) }
11 a yes b no c no d yes
e no
f yes
12 a a 2 b b 2 c √a 2 + b 2
13 2x 2 = c 2
14 a Area of triangle = c 2
Area of 4 outside triangles = 4 × 1 × base × height = 2ab
2
Total area of outside square = (a + b) 2 = a 2 + 2ab + b 2
Area of inside square = Area (outside square) − 4 triangles
= a 2 + 2ab + b 2 − 2ab
= a 2 + b 2
Comparing results from the first and last steps gives
c 2 = a 2 + b 2 .
Exercise 3L
1 a yes b no c no d yes
2 a 3.16 b 5.10 c 8.06 d 15.17
3 a w 2 = 3 2 + 5 2
b x 2 = 9 2 + 7 2
c m 2 = 8 2 + 8 2
d x 2 = 7 2 + 9.4 2
4 a 5 b 25 c 41
d 20 e 45 f 61
5 a 9.22 b 5.39 c 5.66
d 3.16 e 4.30 f 37.22
6 3.16 m or 316 cm
7 139 cm
8 5.5 km
9 3.88 cm
10 a 2nd line is incorrect, cannot take the square root of
each term.
b 2nd line is incorrect, cannot add 3 2 + 4 2 to get 7 2 .
c Last line should say ∴ c = √29.
11 a 3 2 + 5 2 ≠ 7 2 b 5 2 + 8 2 ≠ 10 2 c 12 2 + 21 2 ≠ 24 2
12 a 8.61 m b 48.59 cm c 18.56 cm
d 22.25 mm e 14.93 m f 12.25 m
Exercise 3M
1 a 9 2 = m 2 + 3 2 b 10 2 = 5 2 + p 2
c 15 2 = w 2 + w 2 d 12 2 = c 2 + 8 2
2 a a = 12 b b = 24
3 a 4 b 9 c 40
d 15 e 16 f 60
4 a 2.24 b 4.58 c 11.49
d 12.65 e 10.72 f 86.60
5 8.94 m
6 12 cm
7 12.12 cm
8 8.49
9 a Should subtract not add 10.
b Should say a = 5.
c Cannot take the square root of each term.
10 a √24 b √3 c √4400
11 a 3.54 b 7.07 c 43.13 d 24.04
12 a 6 2 + 8 2 = 10 2
b It is a multiple of (3, 4, 5).
c (9, 12, 15), (12, 16, 20), (15, 20, 25)
d (8, 15, 17)
e (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25),
(9, 40, 41), etc.
Puzzles and challenges
1 10 cm each side
2 Yes, 1 L will overflow.
3 1 2
4 √3 ≈ 1.73 m
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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