如图,在直角梯形ABCD中,ad‖bc 角bad等于90°对角线bd垂直dc,ad等于4 bc等于9 则bd等于

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如图,在直角梯形ABCD中,ad‖bc 角bad等于90°对角线bd垂直dc,ad等于4 bc等于9 则bd等于
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如图,在直角梯形ABCD中,ad‖bc 角bad等于90°对角线bd垂直dc,ad等于4 bc等于9 则bd等于
如图,在直角梯形ABCD中,ad‖bc 角bad等于90°对角线bd垂直dc,ad等于4 bc等于9 则bd等于

如图,在直角梯形ABCD中,ad‖bc 角bad等于90°对角线bd垂直dc,ad等于4 bc等于9 则bd等于
BD^2 + DC^2 = BC^2 = 9^2
即 BD^2 + DC^2 = 81-------(1)
过D作DE⊥BC交BC于E
则 BE = AD = 4,CE = BC - BE =9 - 4 = 5
BD^2 - BE^2 = DE^2 = DC^2 -CE^2
即 BD^2 - 4^2 = DC^2 - 5^2
整理得 BD^2 - DC^2 = -9------(2)
(1)+(2)得 2BD^2 = 72
BD^2 =36
BD = 6