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In a triangle ABC right angled at A.the length of altitude from A and length of internal bisector of A are 3 and 4 respectively.find the length of median through A?
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In a triangle ABC right angled at A.the length of altitude from A and ...
Given information:
- Triangle ABC is right-angled at A.
- Length of altitude from A = 3 units.
- Length of internal bisector of A = 4 units.
To find:
Length of median through A.
Solution:
Step 1: Understanding the problem
- In a triangle, the median is a line segment that connects a vertex to the midpoint of the opposite side.
- We are given the lengths of the altitude from A and the internal bisector of A.
- We need to find the length of the median through A.
Step 2: Drawing the triangle
- Draw a triangle ABC with right angle at A.
- Label the length of the altitude from A as 3 units.
- Label the length of the internal bisector of A as 4 units.
Step 3: Solving the problem
- Since triangle ABC is right-angled at A, the altitude from A divides the triangle into two smaller triangles, let's call them ABD and ACD.
- Let's assume the length of the median through A is x units.
- In triangle ABD, the median divides the side BD into two equal parts, each with length x/2.
- In triangle ACD, the median divides the side CD into two equal parts, each with length x/2.
- The altitude from A divides the side BC into two parts, one with length 3 and the other with length (x-3).
- Using the property of the internal bisector, we can write the equation: (x-3)/4 = 3/4.
- Solving this equation, we get x-3 = 9, which gives x = 12.
Step 4: Answer
- The length of the median through A is 12 units.
- Triangle ABC is right-angled at A.
- Length of altitude from A = 3 units.
- Length of internal bisector of A = 4 units.
To find:
Length of median through A.
Solution:
Step 1: Understanding the problem
- In a triangle, the median is a line segment that connects a vertex to the midpoint of the opposite side.
- We are given the lengths of the altitude from A and the internal bisector of A.
- We need to find the length of the median through A.
Step 2: Drawing the triangle
- Draw a triangle ABC with right angle at A.
- Label the length of the altitude from A as 3 units.
- Label the length of the internal bisector of A as 4 units.
Step 3: Solving the problem
- Since triangle ABC is right-angled at A, the altitude from A divides the triangle into two smaller triangles, let's call them ABD and ACD.
- Let's assume the length of the median through A is x units.
- In triangle ABD, the median divides the side BD into two equal parts, each with length x/2.
- In triangle ACD, the median divides the side CD into two equal parts, each with length x/2.
- The altitude from A divides the side BC into two parts, one with length 3 and the other with length (x-3).
- Using the property of the internal bisector, we can write the equation: (x-3)/4 = 3/4.
- Solving this equation, we get x-3 = 9, which gives x = 12.
Step 4: Answer
- The length of the median through A is 12 units.
Community Answer
In a triangle ABC right angled at A.the length of altitude from A and ...
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In a triangle ABC right angled at A.the length of altitude from A and length of internal bisector of A are 3 and 4 respectively.find the length of median through A?
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In a triangle ABC right angled at A.the length of altitude from A and length of internal bisector of A are 3 and 4 respectively.find the length of median through A? 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 In a triangle ABC right angled at A.the length of altitude from A and length of internal bisector of A are 3 and 4 respectively.find the length of median through A? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle ABC right angled at A.the length of altitude from A and length of internal bisector of A are 3 and 4 respectively.find the length of median through A?.
In a triangle ABC right angled at A.the length of altitude from A and length of internal bisector of A are 3 and 4 respectively.find the length of median through A? 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 In a triangle ABC right angled at A.the length of altitude from A and length of internal bisector of A are 3 and 4 respectively.find the length of median through A? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a triangle ABC right angled at A.the length of altitude from A and length of internal bisector of A are 3 and 4 respectively.find the length of median through A?.
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