Question

En dos triangulos semejantes ABC, A'B'C, AB=6m, BC=7m, CA=8m, A'B'=9m. Calcular A'C y B'C' el area el area de los dos triangulos

Answer 1

Solución:

Son triángulos semejantes, lados en misma proporción

6 / 9 = 7 / B'C'
B'C' = 9 × 7 / 6
B'C' = 63 / 6
B'C' = 21 / 2
B'C' = 10.5 m

6 / 9 = 8 / A'C'
A'C' = 9 × 8 / 6
A'C' = 72 / 6
A'C' = 12 m

Area ΔABC = √(s(s - a)(s - b)(s - c))
AB = a = 6
BC = b = 7
CA = c = 8

semiperimetro = s = (a + b + c) / 2
s = (6 + 7 + 8) / 2
s = 21 / 2
s = 10.5

Area ΔABC = √(10.5(10.5 - 6)(10.5 - 7)(10.5 - 8))
Area ΔABC = √(10.5(4.5)(3.5)(2.5))

Area ΔABC = 20.33 m²

Area ΔA'B'C' = √(s'(s' - a')(s' - b')(s' - c'))
A'B' = a' = 9
B'C' = b' = 10.5
A'C' = c' = 12

semiperimetro = s' = (a' + b' + c') / 2
s' = (9 + 10.5 + 12) / 2
s' = 31.5 / 2
s' = 15.75

Area ΔA'B'C' = √(15.75(15.75 - 9)(15.75 - 10.5)(15.75 - 12))
Area ΔA'B'C' = √(15.75(6.75)(5.25)(3.75))

Area ΔA'B'C' = 45.75 m²