Answer:
≈ 9.27
Step-by-step explanation:
suppose BC:a AC:b AB: c AE: ma BD: mb CF: mc
ma = mb = 3 mc = 2
by the Apollonius' Theorem:
b² + c² = 2(ma² + (a/2)² = 1/2*a² + 2ma² = 1/2*a² + 18 ...(1)
a² + c² = 2(mb² + (b/2)² = 1/2*b² + 2mb² = 1/2*b² + 18 ...(2)
a² + b² = 2(mc² + (c/2)² = 1/2*c² + 2mc² = 1/2*c² + 8 ...(3)
2(a² + b² + c²) = 1/2 (a² + b² + c²) + 44 ...(1)+(2)+(3)
a² + b² + c² = 88/3 ...(4)
(4)-(3): c² = 88/3 - 1/2*c² - 8 = - 1/2*c² + 64/3
3/2*c² = 64/3 c² = 128/9 c = 8√2 / 3 ≈ 3.77
Use the same calculation: a = b = 2√17/3 ≈ 2.75
perimeter ≈ 2.75+2.75+3.77 ≈ 9.27
I think you have to check the accuracy of the calculation. If there is calculation error, I apologize. But.. the process should be right.
