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In triangle ABC, E is the mid point of the median AD. What will be the ratio of the area of triangle BED and triangle ABC.?
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In triangle ABC, E is the mid point of the median AD. What will be the...
AD is the median of ΔABC. Therefore, it will divide ΔABC into two triangles of equal area.
∴ Area (ΔABD) = Area (ΔACD)
⇒Area (ΔABD ) = (1/2) area (Δ ABC) ------------(1)
In ΔABD, E is the mid-point of AD.
Therefore, BE is the median.
∴ Area (ΔBED) = Area (ΔABE)
Area (ΔBED) = (1/2)Area (ΔABD)
Area (ΔBED) = (1/2 ) x(1/2) Area (ΔABC) [From (1)]
∴ Area (ΔBED) = (1/4)Area (ΔABC).
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In triangle ABC, E is the mid point of the median AD. What will be the...
Understanding the Triangle and Median
In triangle ABC, let D be the midpoint of side BC. The median AD divides triangle ABC into two smaller triangles, ABD and ACD, which have equal areas.
Midpoint E of Median AD
- E is the midpoint of median AD.
- This means AE = ED, and triangle ABE is similar to triangle ABD.
Area Calculation
- The area of triangle ABC can be expressed as the sum of the areas of triangles ABD and ACD.
- Since D is the midpoint of BC, the area of triangle ABD is equal to the area of triangle ACD.
Area of Triangle BED
- Triangle BED is formed by connecting B, E, and D.
- Since E is the midpoint of AD, triangle BED has half the height of triangle ABD, while the base BD remains the same.
Ratio of Areas
- The area of triangle BED can be expressed as half of the area of triangle ABD.
- Therefore, the area of triangle BED is 1/4 the area of triangle ABC (since triangle ABC = triangle ABD + triangle ACD).
Final Ratio
- The ratio of the area of triangle BED to the area of triangle ABC is 1:4.
This result highlights the geometric properties of medians and midpoints in triangles, and how they affect area relationships within the triangle.
In triangle ABC, let D be the midpoint of side BC. The median AD divides triangle ABC into two smaller triangles, ABD and ACD, which have equal areas.
Midpoint E of Median AD
- E is the midpoint of median AD.
- This means AE = ED, and triangle ABE is similar to triangle ABD.
Area Calculation
- The area of triangle ABC can be expressed as the sum of the areas of triangles ABD and ACD.
- Since D is the midpoint of BC, the area of triangle ABD is equal to the area of triangle ACD.
Area of Triangle BED
- Triangle BED is formed by connecting B, E, and D.
- Since E is the midpoint of AD, triangle BED has half the height of triangle ABD, while the base BD remains the same.
Ratio of Areas
- The area of triangle BED can be expressed as half of the area of triangle ABD.
- Therefore, the area of triangle BED is 1/4 the area of triangle ABC (since triangle ABC = triangle ABD + triangle ACD).
Final Ratio
- The ratio of the area of triangle BED to the area of triangle ABC is 1:4.
This result highlights the geometric properties of medians and midpoints in triangles, and how they affect area relationships within the triangle.
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In triangle ABC, E is the mid point of the median AD. What will be the ratio of the area of triangle BED and triangle ABC.?
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In triangle ABC, E is the mid point of the median AD. What will be the ratio of the area of triangle BED and triangle ABC.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In triangle ABC, E is the mid point of the median AD. What will be the ratio of the area of triangle BED and triangle ABC.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In triangle ABC, E is the mid point of the median AD. What will be the ratio of the area of triangle BED and triangle ABC.?.
In triangle ABC, E is the mid point of the median AD. What will be the ratio of the area of triangle BED and triangle ABC.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In triangle ABC, E is the mid point of the median AD. What will be the ratio of the area of triangle BED and triangle ABC.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In triangle ABC, E is the mid point of the median AD. What will be the ratio of the area of triangle BED and triangle ABC.?.
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