Matematika kelas 8 hal 29 semester 2
Matematika kelas 8 hal 29 semester 2
Melengkapi tabel!
p q (p²+q²) (p²-q²) 2pq Hubungan Tripel Pythagoras
3 2 3²+2²=13 3²-2²=5 2×(3×2)=12 13²=5²+12² 13,5,12
4 1 4²+1²=17 4²-1²=15 2×(4×1)=8 17²=15²+8² 17,15,8
4 2 4²+2²=20 4²-2²=12 2×(4×2)=16 20²=12²+16² 20,12,16
4 2 4²+3²=25 4²-3²=7 2×(4×3)=24 25²=7²+24² 25,7,24
5 1 5²+1²=26 5²-1²=24 2×(5×1)=10 26²=24²+10² 26,24,10
5 2 5²+2²=29 5²-2²=21 2×(5×2)=20 29²=21²+20² 29,21,20
5 3 5²+3²=34 5²-3²=16 2×(5×3)=30 34²=16²+30² 34,16,30
5 4 5²+4²=41 5²-4²=9 2×(5×4)=40 41²=9²+40² 41,9,40
Berikut perhitungan detail jawaban di atas.
Pembahasan
p = 3, q = 2
(p² + q²) = 3² + 2² = 9 + 4 = 13
(p² – q²) = 3² – 2² = 9 – 4 = 5
2pq = 2 × (3 × 2) = 2 (6) = 12
Hubungan: 13² = 5² + 12²
Bukti:
169 = 25 + 144
169 = 169
Triple Pythagoras: 13, 5, 12
p = 4, q = 1
(p² + q²) = 4² + 1² = 16 + 1 = 17
(p² – q²) = 4² – 1² = 16 – 1 = 15
2pq = 2 × (4 × 1) = 2 (4) = 8
Hubungan: 17² = 15² + 8²
Bukti:
286 = 225 + 64
286 = 286
Triple Pythagoras: 17, 15, 8
p = 4, q = 2
(p² + q²) = 4² + 2² = 16 + 4 = 20
(p² – q²) = 4² – 2² = 16 – 4 = 12
2pq = 2 × (4 × 2) = 2 (8) = 16
Hubungan: 20² = 12² + 16²
Bukti:
400 = 144 + 256
400 = 400
Triple Pythagoras: 20, 12, 16
p = 4, q = 3
(p² + q²) = 4² + 3² = 16 + 9 = 25
(p² – q²) = 4² – 3² = 16 – 9 = 7
2pq = 2 × (4 × 3) = 2 (12) = 24
Hubungan: 25² = 7² + 24²
Bukti:
625 = 49 + 576
625 = 625
Triple Pythagoras: 25, 7, 24
p = 5, q = 1
(p² + q²) = 5² + 1² = 25 + 1 = 26
(p² – q²) = 5² – 1² = 25 – 1 = 24
2pq = 2 × (5 × 1) = 2 (5) = 10
Hubungan: 26² = 24² + 10²
Bukti:
676 = 576 + 100
676 = 676
Triple Pythagoras: 26, 24, 10
p = 5, q = 2
(p² + q²) = 5² + 2² = 25 + 4 = 29
(p² – q²) = 5² – 2² = 25 – 4 = 21
2pq = 2 × (5 × 2) = 2 (10) = 20
Hubungan: 29² = 21² + 20²
Bukti:
841 = 441 + 400
841 = 841
Triple Pythagoras: 29, 21, 20
p = 5, q = 3
(p² + q²) = 5² + 3² = 25 + 9 = 34
(p² – q²) = 5² – 3² = 25 – 9 = 16
2pq = 2 × (5 × 3) = 2 (15) = 30
Hubungan: 34² = 16² + 30²
Bukti:
1156 = 256 + 900
1156 = 1156
Triple Pythagoras: 34, 16, 30
p = 5, q = 4
(p² + q²) = 5² + 4² = 25 + 16 = 41
(p² – q²) = 5² – 4² = 25 – 16 = 9
2pq = 2 × (5 × 4) = 2 (20) = 40
Hubungan: 41² = 9² + 41²
Bukti:
1681 = 81 + 1600
1681 = 1681
Triple Pythagoras: 41, 9, 40
Pelajari lebih lanjut
1. Materi tentang Pythagoras, soal membuat sketsa dan menentukan jarak: brainly.co.id/tugas/21699262
2. Menentukan tinggi segitiga: brainly.co.id/tugas/8693834
3. Pasangan sisi segitiga Phytagoras: brainly.co.id/tugas/5919334
Detail jawaban
Kelas: 8
Mapel: Matematika
Bab: Teorema Pythagoras
Kode: 8.2.4