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109學測數學考科-D


<選填題>平面上有一等形 \(ABCD\),其中 \(AB=BC=\sqrt{2}\),\(\overline{AD}=\overline{CD}=2\),\(\angle BAD=135^\circ\)。則 \(\overline{AC}=\) __________(化為最簡根式)

答案

由餘弦定理得 \(\overline{BD} = \sqrt{10}\)。等形面積為2,又面積 = \(\frac{1}{2} \times AC \times BD\),得 \(AC = \frac{4}{\sqrt{10}} = \frac{2\sqrt{10}}{5}\)。答案:\(\frac{2\sqrt{10}}{5}\) 報錯
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