In Delta ABC a line parallel to side BC cuts the side AB and AC at points D and E respectively and a...........

Quantitative Aptitude (CPO) Coordinate Geometry

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 cm2, then what is the area (in cm2) of quadrilateral DECB?

192

120

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Explanation:

- Parallel Line Divides Triangle: In ?ABC, a line parallel to BC divides AB in the ratio of 1:4 at point D.

- Similarity and Area Ratio: Since DE is parallel to BC, ?ADE is similar to ?ABC. The whole base AB is divided into the ratio 1:4, making AD:AB as 1:5.

- Proportional Area Calculation: The area of ?ADE is (1/5)^2 of the area of ?ABC due to the squared factor involved in area calculations when sides are in ratio.

- Area of ?ADE: The area is (1/25) of ?ABC, which equals 8 cm² (since 200/25 = 8).

- Area of Quadrilateral DECB: Subtract the area of ?ADE from ?ABC; thus, 200 - 8 = 192 cm².

- Option 1: 192: This matches the calculated area of quadrilateral DECB.

- Option 2: 50: Incorrect based on calculation.

- Option 3: 120: Incorrect based on calculation.

- Option 4: 96: Incorrect based on calculation.