小弟我一直看不出來說有什麼方法可解,麻煩一下各位幫幫忙. 謝謝.
梯形abcd,ab邊平行於cd邊. 兩個對角線交叉點為e點. 三角形abc面積為32,三角形cde面積為50. 求梯形面積.
小弟我一直看不出來說有什麼方法可解,麻煩一下各位幫幫忙. 謝謝.
小弟我一直看不出來說有什麼方法可解,麻煩一下各位幫幫忙. 謝謝.
cde = cd * h1 / 2 = 50
abe = ab * h2 / 2 = x
it's trivial that
50 : x = h1^2 : h2^2
and
abc = abe * (h1 + h2) / h2 = x * (1 + h1 / h2) = 32
=> h1 / h2 = (32 - x) / x
=> (h1 / h2)^2 = (32 - x)^2 / x^2 = 50 / x
=> x^2 - 114x + 1024 = 0
find x and then the area abcd = 50 + 32 * 2 - x
because abc = abd = 32
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