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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
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)
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)
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