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JANGAN NGASAL
K = 36 cm
L = 54 cm²
Penjelasan dengan langkah-langkah:
PR² = PQ² + QR²
(6x + 3)² = (4x + 1)² + (7x - 2)²
36x² + 36x + 9 =16x² + 8x + 1 + 49x² - 28x + 4
36x² + 36x + 9 = 65x² - 20x + 5
36x² - 65x² + 36x + 20x + 9 - 5 = 0
-29x² + 56x + 4 = 0
29x² - 56x + 4 = 0
(29x + 2)(x - 2) = 0
29x + 2 = 0 atau x - 2 = 0
29x = -2. x = 2
x = -2/29
x negatif tidak mungkin, jadi yang memenuhi syarat x = 2
PQ = 4x + 1 = 4 . 2 + 1 = 9 cm
QR = 7x - 2 = 7 . 2 - 1 = 12 cm
PR = 6x + 3 = 6 . 2 + 3 = 15 cm
• L = 1/2 x PQ x QR
= 1/2 x 9 x 12
= 54 cm²
• K = PQ + QR + PR
= 9 + 12 + 15
= 36 cm
Penjelasan dengan langkah-langkah:
Rumus phytagoras
PQ² + QR² = PR²
[tex] {(4x + 1)}^{2} + {(7x - 2)}^{2} = {(6x + 3)}^{2} [/tex]
[tex](16 {x}^{2} + 8x + 1) + (49 {x}^{2} - 28x + 4) = 36 {x}^{2} + 36x + 9[/tex]
[tex]16 {x}^{2} + 49 {x}^{2} + 8x - 28x + 1 + 4 = 36 {x}^{2} + 36x + 9[/tex]
[tex]65 {x}^{2} - 20x + 5 = 36 {x}^{2} + 36x + 9[/tex]
[tex]65 {x}^{2} - 36 {x}^{2} - 20x - 36x + 5 - 9 = 0[/tex]
[tex]29 {x}^{2} - 56x - 4 = 0[/tex]
[tex](29x + 2)(x - 2) = 0[/tex]
Nilai x1
[tex]29x + 2 = 0 \\ \\ 29x = - 2 \\ \\ x = - \frac{2}{29} [/tex]
Nilai x2
[tex]x - 2 = 0 \\ \\ x = 2[/tex]
Subtitisikan nilai x = 2
PQ
[tex] = 4x + 1 \\ \\ = 4(2) + 1 \\ \\ = 8 + 1 \\ \\ = 9 \: cm[/tex]
QR
[tex]7x - 2 \\ \\ = 7(2) - 2 \\ \\ = 14 - 2 \\ \\ = 12 \: cm[/tex]
PR
[tex] = 6x + 3 \\ \\ = 6(2) + 3 \\ \\ = 12 + 3 \\ \\ = 15 \: cm[/tex]
Luas PQR
[tex] = \frac{1}{2} \times pq \times qr \\ \\ = \frac{1}{2} \times 9 \times 12 \\ \\ = 9 \times 6 \\ \\ = 54 \: {cm}^{2} [/tex]
Keliling PQR
[tex] = pq + qr + pr \\ \\ = 9 + 12 + 15 \\ \\ = 36 \: cm[/tex]
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