Diketahui : Segitiga ABC, Siku siku C, sisi sisinya membentuk barisan aritmatika Panjang AB = 10 cm Ditanyakan : a. Panjang AC dan BC b. Keliling Segitiga ABC c

mis. AC = suku ke 1 = a, BC = suku ke 2 = a+b, maka AB = suku ke 3 = a+2b = 10.

a + 2b = 10
a = 10 - 2b
[tex] {(a + 2b)}^{2} = {a}^{2} + {(a + b)}^{2} \\ {10}^{2} = {(10 - 2b)}^{2} + {(10 - b)}^{2} \\ 100 = 100 - 40b + 4 {b}^{2} + 100 - 20b + {b}^{2} \\5 {b}^{2} - 60b + 100 = 0 \\ {b}^{2} - 12b + 20 = 0 \\ (b - 10)(b - 2) = 0 \\ b = 10 \: (tidak \: memenuhi)\\ b = 2[/tex]
AC = a = 10 - 4 = 6 cm
BC = a + b = 6 + 2 = 8 cm
keliling = 6 + 8 + 10 = 24 cm
luas = 6 × 8 ÷ 2 = 24 cm^2