Question

In a ∆, is the median. Show that- AB + BC + AC > 2 AD.​

Answer 1

Step-by-step explanation:

Proved that from triangle ABC where AD is median, AB + BC + CA > 2AD

Solution:

Consider triangle ABC where AD is median

The diagram is attached above

We will be using the property of triangle which says SUM OF TWO SIDES OF TRAINGLE IS ALWAYS GRATER THAN THIRD SIDE.

Considering triangle ABD

Using above property of triangle related to relation between sum of two sides and third side we can say that

AB + BD > AD ---(1)

Considering triangle ACD

Using above property of triangle related to relation between sum of two sides and third side we can say that

AC+DC> AD ---(2)

On adding equation (1) and (2), we get

(AB + BD) + (AC + DC ) > AD + AD

=> AB + (BD+ DC ) + AC > 2AD

=> AB + BC + CA > 2AD

Hence proved that from triangle ABC where AD is median, AB + BC + CA > 2AD

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