In triangle ABC,AM is median .If BC=16cm ,AB squre +AC square =200cm then AM =?
Answers
If BC = 16 cm, AB² + AC² = 200 cm then AM is equal to 6 cm.
Step-by-step explanation:
It is given that,
In ∆ ABC,
AM is a median
BC = 16 cm
AB² + AC² = 200 cm
We know that the median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side.
∴ BM = MC = ½ * BC = ½ * 16 = 8 cm …… (i)
Also, the one of the property of the median says that the sum of the squares of any two sides of the triangle is equal to twice the square of half the third side and twice the square of the median bisecting the third side. This theorem is known as Apollonius Theorem.
∴ AB² + AC² = 2AM² + 2MC²
⇒ AB² + AC² = 2(AM² + MC²)
⇒ 200 = 2(AM² + 8²) …… [since AB² + AC² = 200 cm (given)]
⇒ 200/2 = AM² + 64
⇒ 100 = AM² + 64
⇒ AM² = 100 – 64
⇒ AM² = 36
⇒ AM = √36
⇒ AM = 6 cm
Thus, AM is equal to 6 cm.
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