cosB =(ab/2)/BC = 3/5
1.当P在AB边上时,L = T
当P在BC边上时,|BP| = T-6
则余弦公式:
L² = |AB|² + |BP|² - 2*|AB| * |BP| * cosB = 36 + (T-6)² - 2 * 6 * (T-6) * 3/5
= T²-96T/5 + 576/5
∴L = √(T²-96T/5 + 576/5)
当P在CA边上时,AP = T-6-5 = T-11
综上,解析式为:
L=T (0≤T≤6)
L = √(T²-96T/5 + 576/5) (6<T≤11)
L=T-11 (11<T≤16)
2.由L = √(T²-96T/5 + 576/5) (6<T≤11)
= √((T-48/5)² + 576/25)
∴当T=48/5时(即AP⊥BC时),L有最小值√(576/25) = 24/5
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