Page 11 - Modul A+1 MM Tingkatan 4

17. Rajah yang diberi menunjukkan sebuah segi empat tepat PQRS. Diberi MS = NP = x cm dan luas S M R
segi tiga MNQ ialah 38 cm . Hitung nilai-nilai x yang mungkin. 9 cm
2
The diagram given shows a rectangle PQRS. Given MS = NP = x cm and the area of triangle MNQ is

BAB 1 38 cm . Calculate the possible values of x. TP 4 N
2
Luas segi empat tepat PQRS/ Area of rectangle PQRS = 12 × 9 = 108 cm 2 P 12 cm Q
1
Luas ∆PQN/ Area of ∆PQN = —x(12) = 6x cm 2
2
)
(
1
1
9
Luas ∆MNS/ Area of ∆MNS = —x(9 – x) = —x – — x cm 2
2
2 2 2
(
)
1
9
Luas ∆QRM/ Area of ∆QRM = —(9)(12 – x) = 54 – —x cm 2
2 2
(
)
) (
1
9
9
108 – 6x – —x – —x – 54 – —x = 38
2
2
2
2
x + x – 42 = 0 ©PAN ASIA PUBLICATIONS
1
54 – 6x + —x = 38
2
2
1
—x – 6x + 16 = 0
2
2
x – 12x + 32 = 0
2
(x – 4)(x – 8) = 0
x = 4 atau/or x = 8
18. Sebidang lot banglo yang berbentuk segi empat tepat mempunyai perimeter 120 m dan luas 884 m .
2
Cari panjang dan lebarnya. y m
A rectangular bungalow lot has perimeter 120 m and area 884 m . Find its length and width. TP 5
2
2(x + y) = 120 KBAT Menganalisis x m
x + y = 60
y = 60 – x
xy = 884
x(60 – x) = 884
60x – x = 884
2
x – 60x + 884 = 0
2
(x – 34)(x – 26) = 0
x = 34 atau/or x = 26
Jika / If x = 34, y = 60 – 34 = 26
Jika / If x = 26, y = 60 – 26 = 34
∴ Panjang ialah 34 m dan lebar ialah 26 m.
∴ Length is 34 m and width is 26 m.
19. Tentukan nilai positif x yang ditunjukkan dalam rajah berikut.
Determine the positive value of x as shown in the following diagrams. TP 5
Contoh/Example (a)
x cm (x + 7) cm
(2x + 3) cm
40 cm
(2x + 3) = x + (x + 7) 2
2
2
4x + 12x + 9 = x + x + 14x + 49
2
2
2
2
(x – 1)(x + 2) cm 2x – 2x – 40 = 0
2
(x – 1)(x + 2) = 40 x – x – 20 = 0
2
x + 2x – x – 2 = 40 (x – 5)(x + 4) = 0
2 x – 5 = 0 atau/or x + 4 = 0
(x – 6)(x + 7) = 0 x = 5 atau/or x = –4
x – 6 = 0 atau/or x + 7 = 0 ∴ Nilai positif x ialah 5.
x = 6 atau/or x = –7 ∴ The positive value of x is 5.
∴ Nilai positif x ialah 6.
∴ The positive value of x is 6.

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