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In the given Fig. if AB = 2, BC = 6, AE = 6, BF = 8, CE = 7, and CF = 7, compute the ratio of the area of quadrilateral ABDE to the area of ACDF. |
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Answer» Given: AB = 2, BC = 6, AE = 6, BF = 8, CE = 7 and CF = 7 Consider ∆AEC and ∆BCF, In ∆AEC, AC = 8, AE = 6, CE = 7 In ∆BCF, BF = 8, BC = 6, CF = 7 ∴ ∆AEC ≅ ∆BCF ∴ Area of ∆AEC = Area of ∆BCF Subtract area of ∆BDC both sides, we get Area of ∆AEC – Area of ∆BDC = Area of ∆BCF – Area of ∆BDC ⇒ Area of quadrilateral ABDE = Area of ∆CDF ∴ The required ratio is 1 : 1 |
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