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標題:

F6 Maths 197

發問:

In the figure, AD:DB = 1:2. AE : EC = 3:2. Area of triangle BDE : Area of triangle ABC = 圖片參考：http://imgcld.yimg.com/8/n/HA00149615/o/701112130064813873411240.jpg

最佳解答:

圖片參考：http://i.imgur.com/zxx4C.jpg 圖片參考：http://i.imgur.com/Mf6k1.gif 補字補字補字補字補字補字補字補字補字補字補字 2011-12-13 19:51:43 補充： a, b是比例常數 2011-12-14 08:27:34 補充： Area of ABC : Area of BDE = 5 : 2 Area of BDE : Area of ABC = 2 : 5

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其他解答:

consider triangle ABE with base AB triangle ADE : triangle BDE = 1 : 2 (both triangle have a same height from E to base AB) consider triangle ABC with base AC triangle ABE : triangle CBE = 3 : 2 (both triangle have a same height from B to base AC) if area ADE = k => area BDE = 2k area ABE = area ADE + area BDE = 3k => area CBE = 2k => area ABC = k + 2k + 3k = 6k area BDE : area ABC = 2k : 6k => 1 : 3 2011-12-14 01:01:52 補充： if area ADE = k => area BDE = 2k area ABE = area ADE + area BDE = 3k => area CBE = 2k => area ABC = 2k + 3k = 5k area BDE : area ABC = 2k : 5k = 2 : 5 2011-12-14 12:42:34 補充： area of triangle = 1/2 x base x height if height is same for both triangle, => ratio of area is equivalent to the ratio of base (don't mix up it with ratio of "SIMILAR" triangle, here is talking about triangles are not similar)