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NTPC Graduate Tier 1 2016 Shift 2 📅 02 Apr, 2016

The area of a triangle ABC is 63 sq. units. Two parallel lines DE, FG, are drawn such that they divide the line segments AB and AC into three equal parts. What is the area of the quadrilateral DEGF?

A
28 sq. units
B
35 sq. units
C
21 sq. units
D
48 sq. units
Result Summary
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NTPC Graduate Tier 1
2016 • 02 Apr, 2016 • Shift 2
The area of a triangle ABC is 63 sq. units. Two parallel lines DE, FG, are drawn such that they divide the line segments AB and AC into three equal parts. What is the area of the quadrilateral DEGF?
Correct Answer
21 sq. units
Geometric Principle: When parallel lines divide the sides of a triangle into three equal parts, they create three similar triangles with scaling ratios of 1:3, ......
Ref/Book : NTPC Graduate Tier 1 2016
Ref. Subject Geometry & Trigonometry
Chapter -
Ref. Topic Geometry
Pg. No -
💡 Analysis & Explanation
Geometric Principle ▼
When parallel lines divide the sides of a triangle into three equal parts, they create three similar triangles with scaling ratios of 1:3, 2:3, and 3:3 relative to the main triangle.
Area Ratio Calculation ▼
The areas of similar triangles are proportional to the square of their sides. Thus, the areas of the top small triangle, the middle triangle (formed by the second parallel line), and the whole triangle are in the ratio 1^2 : 2^2 : 3^2, which is 1 : 4 : 9.
Quadrilateral Area Deduction ▼
The quadrilateral DEGF is the area between the first and second parallel lines. Its area corresponds to the difference between the middle triangle (ratio 4) and the top small triangle (ratio 1). Area ratio = 4 - 1 = 3 units.
Final Calculation ▼
If 9 units equal 63 sq. units, then 1 unit equals 7 sq. units. The area of quadrilateral DEGF is 3 units * 7 = 21 sq. units.
Conclusion ▼
The exact area is 21 sq. units.
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