Question

A right angle triangle ABC D and e are the points on AB and BC ad and CE are the median if ad is equals to 3 root 5 upon 2 and ac is equals to 5 cm then find ce??? ​

Answer 1

The length of the median CE in the given right-angled triangle ABC with D and E as midpoints on AB and BC respectively is equal to the length of median AD, which is \( \frac{3\sqrt{5}}{2} \) cm.

Step-by-step explanation:

The question involves finding the length of the median CE in a right-angled triangle ABC where D and E are the midpoints on AB and BC, respectively, and AD is given. Since AD is the median, it means it bisects AC. Given that AC is 5 cm and AD is \( \frac{3\sqrt{5}}{2} \) cm, we must first establish the relationship between the median and the sides of the triangle. In a right-angled triangle, the median to the hypotenuse (AC in this case) is half the length of the hypotenuse. Hence, AD would be \( \frac{1}{2} \times AC \). Knowing this, we can calculate the length of CE, which is also a median and by properties of medians in a triangle, CE should be equal to AD. Therefore, CE is \( \frac{3\sqrt{5}}{2} \) cm.