1. In ΔABC, a line parallel to side BC cuts the side AB and AC at points D and E respectively and also point D divide AB in the ratio of 1 : 4. If area of ΔABC is 200 cm$$^{2}$$, then what is the area (in cm$$^{2}$$) of quadrilateral DECB?
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By: anil on 05 May 2019 02.25 am
The ratio of AD and DB = 1: 4 (given) Hence, the ratio of AD and AB can be taken as 1 : 5 $$ riangle$$ ADE, $$ riangle$$ ABC are similar triangles, so their areas will be in the ratio of 1 : 25 ($$ecause$$ AD : AB = 1 : 5) Total area of the triangle = 200 25x = 200 (or) x = 8 cm$$^{2}$$ Now, Area of ADE = 8 cm$$^{2}$$ and Area of DECB = 200 - 8 = 192 cm$$^{2}$$ Hence, option A is the correct answer.
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