Question

In Triangle ABC , D is the mid-point of side BC. Find the length of side AB.

• A. $\sqrt{24}units$
• B. $\sqrt{26}units$
• C. 4 units
• D. 5 units

Answer 1

The correct option is B

$\sqrt{26}units$

In the given figure, since D is the mid-point of side BC, AD is a Median.

Using Appollonius theorem,
we have,

$A{B}^2+A{C}^2=2(B{D}^2+A{D}^2)\Rightarrow A{B}^2+(12{)}^2=2(36+49)A{B}^2+144=170A{B}^2=26\Rightarrow AB=\sqrt{26}units$