Question

Diketahui segitiga ABC dengan panjang AB = 7 cm, BC = 10, dan AC = 13 cm. panjang jari-jari lingkaran luarnya adalah...cm

a. 90/24 akar3
b. 91/24 akar3
c. 90/24 akar2
d. 91/24 akar2

Answer 1

S = 1/2 × (a + b + c)
s = 1/2 × (7 + 10 +13)
= 1/2 × 30
= 15 cm

L ∆ ABC = √[s (s - a)(s - b)(s - c)]
= √[15 (15 - 7)(15 - 10)(15 - 13)]
= √]15 (8)(5)(2)]
= √1200
= 20√3 cm²

r luar = abc / (4 L∆)
= 7 × 10 × 13 / (4 × 20√3)
= 91 / 8√3 × √3/√3
= 91 × √3 / (8 × 3)
= 91/24 √3 cm