4 TIPE
TEOREMA PYTHAGORAS
Teorema Pythagoras sering kita
gunakan untuk mencari panjang sisi segi tiga, serta mencari panjang diagonal
segi empat. Pada dasarnya Teorema Pythagoras dirumuskan sebagai berikut :
a2
+ b2 = c2 atau c =√ a2 + b2
keterangan:
a =
sisi tegak
b =
sisi alas
c = sisi miring
contoh
soal :
1.
Diketahui sebuah segi tiga dengan panjang alas 3 cm dan
tinggi 4 cm. Tentukan panjang sisi miringnya ?
Diketahui :
a = 3 cm
b = 4 cm
Ditanyakan :
C =…?
Jawab :
=√ 32
+ 42
=√ 9 + 16
=√25
=5
2.
Diketahui sebuah persegi panjang dengan lebar 5 cm dan
panjang 12 cm. Berapakah panjang diagonalnya ?
Diketahui :
a = 5 cm
b = 12 cm
Ditanyakan :
C =…?
Jawab :
=√ 52
+ 122
=√ 25+ 144
=√169
=13
3.
Diketahui sebuah segi tiga dengan panjang alas 7 cm dan
tinggi 24 cm. Carilah panjang sisi miringnya ?
Diketahui :
a = 7 cm
b = 24 cm
Ditanyakan :
C =…?
Jawab :
=√ 72
+242
=√ 49+ 576
=√625
=25
4.
Diketahui sebuah persegi panjang dengan lebar 8 cm dan
panjang 15 cm. Berapakah panjang diagonalnya ?
Diketahui :
a = 8 cm
b = 15 cm
Ditanyakan :
C =…?
Jawab :
=√ 82
+ 152
=√ 64+ 225
=√289
=17
Soal-soal di atas menunjukkan bahwa
Teorema Pythagoras dibagi menjadi 4 tipe sehinga dapat digambarkan seperti
table dibawah ini
4 MACAM TIPE TEOREMA
PYTHAGORAS
|
|||||||||||||
NO
|
TIPE 1
|
TIPE 2
|
TIPE 3
|
TIPE 4
|
|||||||||
a
|
b
|
c
|
a
|
b
|
c
|
a
|
b
|
c
|
a
|
b
|
c
|
||
1
|
3
|
4
|
5
|
5
|
12
|
13
|
7
|
24
|
25
|
8
|
15
|
17
|
|
2
|
6
|
8
|
10
|
10
|
24
|
26
|
14
|
48
|
50
|
16
|
30
|
34
|
|
3
|
9
|
12
|
15
|
15
|
36
|
39
|
21
|
72
|
75
|
24
|
45
|
51
|
|
4
|
12
|
16
|
20
|
20
|
48
|
52
|
28
|
96
|
100
|
32
|
60
|
68
|
|
5
|
15
|
20
|
25
|
25
|
60
|
65
|
35
|
120
|
125
|
40
|
75
|
85
|
|
6
|
18
|
24
|
30
|
30
|
72
|
78
|
42
|
144
|
150
|
48
|
90
|
102
|
|
7
|
21
|
28
|
35
|
35
|
84
|
91
|
49
|
168
|
175
|
56
|
105
|
119
|
|
8
|
24
|
32
|
40
|
40
|
96
|
104
|
56
|
192
|
200
|
64
|
120
|
136
|
|
9
|
27
|
36
|
45
|
45
|
108
|
117
|
63
|
216
|
225
|
72
|
135
|
153
|
|
10
|
30
|
40
|
50
|
50
|
120
|
130
|
70
|
240
|
250
|
80
|
150
|
170
|
|
11
|
33
|
44
|
55
|
55
|
132
|
143
|
77
|
264
|
275
|
88
|
165
|
187
|
|
12
|
36
|
48
|
60
|
60
|
144
|
156
|
84
|
288
|
300
|
96
|
180
|
204
|
|
13
|
39
|
52
|
65
|
65
|
156
|
169
|
91
|
312
|
325
|
104
|
195
|
221
|
|
14
|
42
|
56
|
70
|
70
|
168
|
182
|
98
|
336
|
350
|
112
|
210
|
238
|
|
15
|
45
|
60
|
75
|
75
|
180
|
195
|
105
|
360
|
375
|
120
|
225
|
255
|
|
16
|
48
|
64
|
80
|
80
|
192
|
208
|
112
|
384
|
400
|
128
|
240
|
272
|
|
17
|
51
|
68
|
85
|
85
|
204
|
221
|
119
|
408
|
425
|
136
|
255
|
289
|
|
18
|
54
|
72
|
90
|
90
|
216
|
234
|
126
|
432
|
450
|
144
|
270
|
306
|
|
19
|
57
|
76
|
95
|
95
|
228
|
247
|
133
|
456
|
475
|
152
|
285
|
323
|
|
20
|
60
|
80
|
100
|
100
|
240
|
260
|
140
|
480
|
500
|
160
|
300
|
340
|
|
21
|
63
|
84
|
105
|
105
|
252
|
273
|
147
|
504
|
525
|
168
|
315
|
357
|
|
22
|
66
|
88
|
110
|
110
|
264
|
286
|
154
|
528
|
550
|
176
|
330
|
374
|
|
23
|
69
|
92
|
115
|
115
|
276
|
299
|
161
|
552
|
575
|
184
|
345
|
391
|
|
24
|
72
|
96
|
120
|
120
|
288
|
312
|
168
|
576
|
600
|
192
|
360
|
408
|
|
25
|
75
|
100
|
125
|
125
|
300
|
325
|
175
|
600
|
625
|
200
|
375
|
425
|
|
26
|
78
|
104
|
130
|
130
|
312
|
338
|
182
|
624
|
650
|
208
|
390
|
442
|
|
27
|
81
|
108
|
135
|
135
|
324
|
351
|
189
|
648
|
675
|
216
|
405
|
459
|
|
28
|
84
|
112
|
140
|
140
|
336
|
364
|
196
|
672
|
700
|
224
|
420
|
476
|
|
29
|
87
|
116
|
145
|
145
|
348
|
377
|
203
|
696
|
725
|
232
|
435
|
493
|
|
30
|
90
|
120
|
150
|
150
|
360
|
390
|
210
|
720
|
750
|
240
|
450
|
510
|
|
31
|
93
|
124
|
155
|
155
|
372
|
403
|
217
|
744
|
775
|
248
|
465
|
527
|
|
32
|
96
|
128
|
160
|
160
|
384
|
416
|
224
|
768
|
800
|
256
|
480
|
544
|
|
33
|
99
|
132
|
165
|
165
|
396
|
429
|
231
|
792
|
825
|
264
|
495
|
561
|
|
34
|
102
|
136
|
170
|
170
|
408
|
442
|
238
|
816
|
850
|
272
|
510
|
578
|
|
35
|
105
|
140
|
175
|
175
|
420
|
455
|
245
|
840
|
875
|
280
|
525
|
595
|
|
36
|
108
|
144
|
180
|
180
|
432
|
468
|
252
|
864
|
900
|
288
|
540
|
612
|
|
37
|
111
|
148
|
185
|
185
|
444
|
481
|
259
|
888
|
925
|
296
|
555
|
629
|
|
38
|
114
|
152
|
190
|
190
|
456
|
494
|
266
|
912
|
950
|
304
|
570
|
646
|
|
39
|
117
|
156
|
195
|
195
|
468
|
507
|
273
|
936
|
975
|
312
|
585
|
663
|
|
40
|
120
|
160
|
200
|
200
|
480
|
520
|
280
|
960
|
1000
|
320
|
600
|
680
|
|
41
|
123
|
164
|
205
|
205
|
492
|
533
|
287
|
984
|
1025
|
328
|
615
|
697
|
|
42
|
126
|
168
|
210
|
210
|
504
|
546
|
294
|
1008
|
1050
|
336
|
630
|
714
|
|
43
|
129
|
172
|
215
|
215
|
516
|
559
|
301
|
1032
|
1075
|
344
|
645
|
731
|
|
44
|
132
|
176
|
220
|
220
|
528
|
572
|
308
|
1056
|
1100
|
352
|
660
|
748
|
|
45
|
135
|
180
|
225
|
225
|
540
|
585
|
315
|
1080
|
1125
|
360
|
675
|
765
|
|
46
|
138
|
184
|
230
|
230
|
552
|
598
|
322
|
1104
|
1150
|
368
|
690
|
782
|
|
47
|
141
|
188
|
235
|
235
|
564
|
611
|
329
|
1128
|
1175
|
376
|
705
|
799
|
|
48
|
144
|
192
|
240
|
240
|
576
|
624
|
336
|
1152
|
1200
|
384
|
720
|
816
|
|
49
|
147
|
196
|
245
|
245
|
588
|
637
|
343
|
1176
|
1225
|
392
|
735
|
833
|
|
50
|
150
|
200
|
250
|
250
|
600
|
650
|
350
|
1200
|
1250
|
400
|
750
|
850
|
|
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