梯形证明题已知梯形的一条对角线垂直于上、下两底,上、下两底与这条对角线的和为12cm,梯形面积为12cm²,求

设梯形为ABCD,AD//BC,AC⊥AD,AC⊥BC,求BD设AD + BC = a,设AC = h根据题目有a+h = 12,ah/2 = 12,ah = 24过D做DE⊥BC的延长线于E∴DE = AC = h∴在Rt△BED中BD2 = BE2 + DE2 = a2 + h2 = (a+h)2-2ah = 122-2×24 = 96∴BD = 4√6 cm