ab = 300 bc = 400 ac = 500 ab/bc = 300/400 a/c = 3/4 a = 3c/4 → given: ac = 500 → c = 500/a a = 1500/4a a² = 1500/4 a² = 375 bc/ac = 400/500 b/a = 4/5 b = 4a/5 b² = 16a²/25 → recall: a² = 375 b² = 16 * 375/25 b² = 240 Recall: a/c = 3/4 c = 4a/3 c² = 16a²/9 → recall: a² = 375 c² = 16 * 375/9 c² = 16 * 125/3 c² = 2000/3 (a + b + c)² = (a + b + c).(a + b + c) (a + b + c)² = a² + ab + ac + ab + b² + bc + ac + bc + c² (a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc (a + b + c)² = a² + b² + c² + 2.(ab + ac + bc) (a + b + c)² = 375 + 240 + (2000/3) + 2.(300 + 500 + 400) (a + b + c)² = 3015 + (2000/3) (a + b + c)² = 11045/3 a + b + c = ± √(11045/3) a + b + c = ± √(5 * 47²/3) a + b + c = ± 47√(5/3) a + b + c = ± 47 * √5 * √3 / 3 a + b + c = ± (47/3).√15
Excelente profe
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ab = 300
bc = 400
ac = 500
ab/bc = 300/400
a/c = 3/4
a = 3c/4 → given: ac = 500 → c = 500/a
a = 1500/4a
a² = 1500/4
a² = 375
bc/ac = 400/500
b/a = 4/5
b = 4a/5
b² = 16a²/25 → recall: a² = 375
b² = 16 * 375/25
b² = 240
Recall: a/c = 3/4
c = 4a/3
c² = 16a²/9 → recall: a² = 375
c² = 16 * 375/9
c² = 16 * 125/3
c² = 2000/3
(a + b + c)² = (a + b + c).(a + b + c)
(a + b + c)² = a² + ab + ac + ab + b² + bc + ac + bc + c²
(a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc
(a + b + c)² = a² + b² + c² + 2.(ab + ac + bc)
(a + b + c)² = 375 + 240 + (2000/3) + 2.(300 + 500 + 400)
(a + b + c)² = 3015 + (2000/3)
(a + b + c)² = 11045/3
a + b + c = ± √(11045/3)
a + b + c = ± √(5 * 47²/3)
a + b + c = ± 47√(5/3)
a + b + c = ± 47 * √5 * √3 / 3
a + b + c = ± (47/3).√15
Gracias 👍🧠❤🙂
Gracias maestro desafio las matematicas y aprendo lo poco que puedo un ruco de 75 años saludos
@@magdalanolara9192 saludos❤✋🧠
Bonito problema
Gracias 🙂❤🧠👍