假設上底為 a、下底為 b、高為 h,則
a + h = 6
b + h = 12
兩式相加可得
(a + b) + 2h = 18 => a + b = (18 - 2h)
梯形面積 = (a + b) × h ÷ 2
= (18 - 2h) × h ÷ 2
= (9 - h) × h
= -h^2 + 9h
= -(h^2 - 9h)
= -(h - 9/2)^2 + 81/4,即當 h = 9/2 時,面積有最大值 = 81/4
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4甲 + 乙 = 80
4x + 乙 = 80 => 乙 = 80 - 4x
乘積 = x(80 - 4x)
= -4x^2 + 80x
= -4(x^2 - 20x)
= -4(x - 10)^2 + 400,即當 x = 10 時,乘積有最大值 = 400
謝謝解答......!