In a triangle ABC, P is the midpoint of BC. If AB = (2x+4) cm, AC = 6 cm and AP ⊥ BC, then the value of x is:
- A3
- B4
- C1
- D2
Solution & Step-by-step Explanation
In △ABC, AP is a median because P is the midpoint of BC.
It is also given that AP⊥BC, meaning AP is an altitude.
When the median and the altitude to a side are the same line segment, the triangle must be isosceles with AB=AC.
Therefore:
2x+4=6
2x=2
x=1
It is also given that AP⊥BC, meaning AP is an altitude.
When the median and the altitude to a side are the same line segment, the triangle must be isosceles with AB=AC.
Therefore:
2x+4=6
2x=2
x=1