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D and E are the points on the sides AB and AC of a triangle ABC such that AD=3 ,BD=5 ,BC=12.8 and DE||BC . then length of DE ?
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D and E are the points on the sides AB and AC of a triangle ABC such t...
GIVEN: In Δ ABC, D and E are points on AB and AC , DE|| BC and AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BE = 5 cm.
In Δ ADE and Δ ABC,
∠ADE =∠ABC (corresponding angles)
[DE || BC, AB is transversal]
∠AED =∠ACB (corresponding angles)
[DE || BC, AC is transversal]
So, Δ ADE ~ Δ ABC (AA similarity)
Therefore, AD/AB = AE/AC = DE/BC [In similar triangles corresponding sides are proportional]
AD/AB = DE/BC
2.4/(2.4 + DB) = 2/5
2.4 x 5 = 2(2.4 + DB)
12 = 4.8 + 2DB
12 - 4.8 = 2DB
7.2 = 2DB
DB = 7.2/2
DB = 3.6 cm
Similarly, AE/AC = DE/BC
3.2/(3.2+EC) = 2/5
3.2 x 5 = 2(3.2+EC)
16 = 6.4 + 2EC
16 - 6.4 = 2EC
9.6 = 2EC
EC = 9.6/2
EC = 4.8 cm
Hence, BD = 3.6 cm and CE = 4.8 cm.
In Δ ADE and Δ ABC,
∠ADE =∠ABC (corresponding angles)
[DE || BC, AB is transversal]
∠AED =∠ACB (corresponding angles)
[DE || BC, AC is transversal]
So, Δ ADE ~ Δ ABC (AA similarity)
Therefore, AD/AB = AE/AC = DE/BC [In similar triangles corresponding sides are proportional]
AD/AB = DE/BC
2.4/(2.4 + DB) = 2/5
2.4 x 5 = 2(2.4 + DB)
12 = 4.8 + 2DB
12 - 4.8 = 2DB
7.2 = 2DB
DB = 7.2/2
DB = 3.6 cm
Similarly, AE/AC = DE/BC
3.2/(3.2+EC) = 2/5
3.2 x 5 = 2(3.2+EC)
16 = 6.4 + 2EC
16 - 6.4 = 2EC
9.6 = 2EC
EC = 9.6/2
EC = 4.8 cm
Hence, BD = 3.6 cm and CE = 4.8 cm.
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
D and E are the points on the sides AB and AC of a triangle ABC such t...
Given Information:
We are given a triangle ABC with points D and E on sides AB and AC respectively. It is given that AD = 3, BD = 5, BC = 12.8, and DE || BC.
To Find:
We need to find the length of DE.
Explanation:
Step 1: Understand the given information:
We are given a triangle ABC with points D and E on sides AB and AC respectively. It is given that AD = 3, BD = 5, BC = 12.8, and DE || BC.
Step 2: Understand the concept of similar triangles:
When two triangles have their corresponding angles equal, they are said to be similar. In similar triangles, the corresponding sides are proportional.
Step 3: Identify the similar triangles:
In the given triangle ABC, we can see that triangle ADE and triangle ABC are similar because angle ADE is equal to angle ABC (alternate interior angles) and angle AED is equal to angle ACB (corresponding angles).
Step 4: Set up proportions:
Since triangle ADE and triangle ABC are similar, we can set up the following proportion using the corresponding sides:
AD / AB = DE / BC
Substituting the given values, we get:
3 / (3 + 5) = DE / 12.8
Simplifying the equation, we have:
3/8 = DE / 12.8
Step 5: Solve for DE:
To find the value of DE, we can cross-multiply and solve for DE:
DE = (3/8) * 12.8
DE = 4.8
Therefore, the length of DE is 4.8 units.
We are given a triangle ABC with points D and E on sides AB and AC respectively. It is given that AD = 3, BD = 5, BC = 12.8, and DE || BC.
To Find:
We need to find the length of DE.
Explanation:
Step 1: Understand the given information:
We are given a triangle ABC with points D and E on sides AB and AC respectively. It is given that AD = 3, BD = 5, BC = 12.8, and DE || BC.
Step 2: Understand the concept of similar triangles:
When two triangles have their corresponding angles equal, they are said to be similar. In similar triangles, the corresponding sides are proportional.
Step 3: Identify the similar triangles:
In the given triangle ABC, we can see that triangle ADE and triangle ABC are similar because angle ADE is equal to angle ABC (alternate interior angles) and angle AED is equal to angle ACB (corresponding angles).
Step 4: Set up proportions:
Since triangle ADE and triangle ABC are similar, we can set up the following proportion using the corresponding sides:
AD / AB = DE / BC
Substituting the given values, we get:
3 / (3 + 5) = DE / 12.8
Simplifying the equation, we have:
3/8 = DE / 12.8
Step 5: Solve for DE:
To find the value of DE, we can cross-multiply and solve for DE:
DE = (3/8) * 12.8
DE = 4.8
Therefore, the length of DE is 4.8 units.
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D and E are the points on the sides AB and AC of a triangle ABC such that AD=3 ,BD=5 ,BC=12.8 and DE||BC . then length of DE ?
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D and E are the points on the sides AB and AC of a triangle ABC such that AD=3 ,BD=5 ,BC=12.8 and DE||BC . then length of DE ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about D and E are the points on the sides AB and AC of a triangle ABC such that AD=3 ,BD=5 ,BC=12.8 and DE||BC . then length of DE ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for D and E are the points on the sides AB and AC of a triangle ABC such that AD=3 ,BD=5 ,BC=12.8 and DE||BC . then length of DE ?.
D and E are the points on the sides AB and AC of a triangle ABC such that AD=3 ,BD=5 ,BC=12.8 and DE||BC . then length of DE ? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about D and E are the points on the sides AB and AC of a triangle ABC such that AD=3 ,BD=5 ,BC=12.8 and DE||BC . then length of DE ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for D and E are the points on the sides AB and AC of a triangle ABC such that AD=3 ,BD=5 ,BC=12.8 and DE||BC . then length of DE ?.
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