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BL and CM are medians of ABC right angled at A and BC =5 cm. If BL =3- 5/2 cm, then the length of CM is
- a)2 5
- b)5 2
- c)10 2
- d)4 5
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
BL and CM are medians of ABC right angled at A and BC =5 cm. If BL =3-...
Here, BC = 5cm
BL = 3 5/2 cm
By using the formula
4(BL2 + CM2) = 5BC2
Most Upvoted Answer
BL and CM are medians of ABC right angled at A and BC =5 cm. If BL =3-...
Understanding Medians in Right-Angled Triangle
In triangle ABC, where angle A is a right angle, we have two medians: BL and CM. The lengths of these medians are crucial for solving the problem.
Given Information
- Length of side BC = 5 cm
- Length of median BL = 3 - 5/2 cm = 3 - 2.5 cm = 0.5 cm
Finding Length of CM
1. Medians in Right-Angled Triangle:
- In any triangle, the median from a vertex to the midpoint of the opposite side can be calculated using the formula, but in a right triangle, it's simpler due to the properties of right angles.
2. Using the Formula:
- The median length from vertex A (right angle) to the hypotenuse BC can be calculated as:
Length of median = 1/2 * sqrt(2AB^2 + 2AC^2 - BC^2)
3. Finding Lengths AB and AC:
- Since we are working with a right angle at A and BC as the hypotenuse, we assume:
- AB = x cm
- AC = y cm
- Using Pythagoras theorem:
x^2 + y^2 = 5^2 = 25
4. Calculating CM:
- The length of CM can also be derived through its relation to the sides.
- For a right triangle, the median to the hypotenuse (CM) is equal to half the length of the hypotenuse:
CM = 1/2 * BC = 1/2 * 5 = 2.5 cm
Final Answer
Thus, the length of median CM = 2.5 cm, which corresponds to option 'A' as 2 5.
In triangle ABC, where angle A is a right angle, we have two medians: BL and CM. The lengths of these medians are crucial for solving the problem.
Given Information
- Length of side BC = 5 cm
- Length of median BL = 3 - 5/2 cm = 3 - 2.5 cm = 0.5 cm
Finding Length of CM
1. Medians in Right-Angled Triangle:
- In any triangle, the median from a vertex to the midpoint of the opposite side can be calculated using the formula, but in a right triangle, it's simpler due to the properties of right angles.
2. Using the Formula:
- The median length from vertex A (right angle) to the hypotenuse BC can be calculated as:
Length of median = 1/2 * sqrt(2AB^2 + 2AC^2 - BC^2)
3. Finding Lengths AB and AC:
- Since we are working with a right angle at A and BC as the hypotenuse, we assume:
- AB = x cm
- AC = y cm
- Using Pythagoras theorem:
x^2 + y^2 = 5^2 = 25
4. Calculating CM:
- The length of CM can also be derived through its relation to the sides.
- For a right triangle, the median to the hypotenuse (CM) is equal to half the length of the hypotenuse:
CM = 1/2 * BC = 1/2 * 5 = 2.5 cm
Final Answer
Thus, the length of median CM = 2.5 cm, which corresponds to option 'A' as 2 5.
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