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In the adjoining figure, angle LMN=90 and MP is a median. If  LM=10 and ,MN=24 then find MP. class 9 correct ans
10
12
24
13


Given the triangle \( \triangle LMN \) with \( \angle LMN = 90^\circ \), \( LM = 10 \), \( MN = 24 \), and \( MP \) is a median, we are asked to find the length of \( MP \).

### Steps to solve:

1. Since \( \angle LMN = 90^\circ \), \( \triangle LMN \) is a right-angled triangle with \( \angle LMN \) being the right angle.

2. To find the length of the hypotenuse \( LN \), use the Pythagorean theorem:
   \[
   LN = \sqrt{LM^2 + MN^2}
   \]
   Substitute the given values:
   \[
   LN = \sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} = 26
   \]
   So, \( LN = 26 \).

3. Since \( MP \) is a median to the hypotenuse \( LN \), in a right-angled triangle, the median to the hypotenuse is always half the length of the hypotenuse. Therefore:
   \[
   MP = \frac{LN}{2} = \frac{26}{2} = 13
   \]

### Correct Answer:
The correct answer is **13**.

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Would you like further details or have any other questions?

Here are some related questions you might be interested in:
1. What is the Pythagorean theorem and when is it used?
2. How do you find the length of a median in a triangle?
3. What properties are unique to medians in right-angled triangles?
4. How can the length of a hypotenuse be calculated in any right triangle?
5. What other methods can be used to find the length of a median?

**Tip:** In any right triangle, the median to the hypotenuse is always half the length of the hypotenuse. This property is unique to right triangles and can be a quick way to solve problems involving medians.

Learn how to find the length of median MP in right triangle LMN with detailed step-by-step solution using the Pythagorean theorem and properties of medians. Suitable for Class 9 students.

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