Question

1. Keliling segitiga ABC=80cm. Jika perbandingan sisinya 8:15:17,tentukan luas segitiga ABC tsb
2.Diketahui panjang sisi segitiga PQR adl (3x+1)cm,(4x-3)cm,dan 2(x-1)cm.Jika keliling=23cm.Tentukanlah panjang sisi terpanjang(sisi miring) dari segitiga PQR?

Answer 1

Nomor 1
keliling = sisi a + sisi b + sisi c
80 = 8y + 15y  + 17y
80 = 40y
80 : 40 = y
2 = y

8y = 8 x 2 = 16 cm
15y = 15 x 2 = 30 cm
17y = 17 x 2 = 34 cm

luas
s = 1/2 keliling = 1/2 x 80 = 40
√s(s-a)(s-b)(s-c)
√40(40-16)(40-30)(40-34)
√40(24) (10) (6)
√2² x 2 x 5 x   2² x 2 x 3 x 2 x 5 x 2 x 3
√2² x 2² x 2² x 2² x 3² x 5² 
2 x 2 x 2 x 2 x 3 x 5
240 cm²

nomor 2
K = sisi a + sisi b + sisi c
23 = 3x + 1 + 4x - 3 + 2x - 2
23 = 9x -4
23 + 4 = 9x
27 = 9x
3 = x

3x + 1 = 3(3) + 1 = 9 + 1 = 10 cm=========> terpanjang
4x - 3 = 4(3) - 3 = 12 - 3 = 9 cm
2x - 2 = 2(3) - 2 = 6 - 2 = 4 cm

Answer 2

1. k = a + b + c
80 = 8x + 15x + 17x
80 = 40x
x = 2 

(segitiga siku2)
L = 1/2.a.t
  = 1/2. 30.16
  = 240 cm^2

2. k = a + b + c
    23 = (3x+1) + (4x-3) + 2(x-1)
     23 = 7x -2 + 2x -2
     23 = 9x - 4
     27 = 9x
     x = 3
 sisi terpanjang 
(3x+1) = 3.3 + 1
          = 10 cm