In triangle ABC, A = 90°, AB = 2.5 and AC = 6. If AD is the median, what is the length of AD?
Question
In triangle ABC,
- A = 90°
- AB = 2.5
- AC = 6
If AD is the median, what is the length of AD?
Solution
In a right triangle, the median on the hypotenuse (which is the line segment connecting the right angle vertex to the midpoint of the hypotenuse) is half the length of the hypotenuse. This is a property of right triangles.
Given that triangle ABC is a right triangle with A = 90°, AB = 2.5 and AC = 6, the hypotenuse BC can be calculated using the Pythagorean theorem:
BC = sqrt(AB^2 + AC^2) BC = sqrt((2.5)^2 + (6)^2) BC = sqrt(6.25 + 36) BC = sqrt(42.25) BC = 6.5
Since AD is the median on the hypotenuse BC, the length of AD is half the length of BC:
AD = BC / 2 AD = 6.5 / 2 AD = 3.25
So, the length of AD is 3.25.
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