Question

If in $△ABC$, D is the midpoint of BC, then the length of AC equals

• A. 26 units
• B. $\sqrt{245}cm$
• C. 145 cm
• D. $\sqrt{145}cm$

Answer 1

The correct option is D $\sqrt{145}cm$

In the given figure, since D is the mid-point of side BC, AD is a median.
From Apollonius's theorem, we have $A{B}^2+A{C}^2=2(B{D}^2+A{D}^2)\Rightarrow 5^2+A{C}^2=2(6^2+7^2)(\because BD=\frac{BC}{2})A{C}^2+25=170A{C}^2=145\Rightarrow AC=\sqrt{145}cm$