Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that AD : BD = 2 : 1 and AE : CE = 2 : 3. If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is
Explanation:
Consider the figure below.
Consider ∆AED and ∆BED. Height of both triangles is same, hence ratio of area will be same as ratio of their base. ∴ Area(∆AED)/Area(∆BED) = AD/BD = 2/1
Area (∆BED) = 8/2 = 4
∴ Area (∆ABE) = 8 + 4 = 12
Now, consider ∆AED and ∆BED. Height of both triangles is same, hence ratio of area will be same as ratio of their base. ∴ Area(∆ABE)/Area(∆CBE) = AE/CE = 2/3
Area (∆CBE) = 3/2 × 12 = 18
∴ Area (∆ABC) = 12 + 18 = 30 sq. cm.
Hence, 30.
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