Multiple Choice Questions on In Delta ABC a line parallel to side BC cuts the side AB and AC at points D and E respectively and a........... for SSC (CPO) Exam Preparation

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Multiple Choice Questions

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) Geometry
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    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

    Correct Answer

    90

    Incorrect Answer

    120

    Incorrect Answer

    96

    Incorrect Answer
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    Explanation:

    - A line parallel to side BC of ?ABC intersects sides AB and AC at points D and E.

    - The point D divides AB in the ratio 1:4, meaning AD/DB = 1/4.

    - The area of ?ABC is given as 200 cm².

    - Since DE || BC, triangles ADE and ABC are similar.

    - Since AD:DB = 1:4, thus area of ?ADE : area of ?ABC = (1/5)² = 1/25.

    - Area of ?ADE = (1/25) * 200 = 8 cm².

    - Area of quadrilateral DECB = Area of ?ABC - Area of ?ADE = 200 - 8 = 192 cm².

    Correct Answer: Option 1 - 192 cm²

    By: Kamal Kashyap
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