Obtain the value of CD, which is the median of the traingle ABC, if AC = 6, CB = 13 and AB = 15.

In a triangle ACB, CD is the median, and sides AC = 6, CB = 13, AB = 15.

The median of the triangle is given by

\$CD = \sqrt{\frac{2(BC) ^2 + 2(AC) ^2 - (AB) ^2}{4}} \$

Substitute the values.

\$\Rightarrow CD = \sqrt{\frac{2(13) ^2 + 2(6) ^2 - (15) ^2}{4}}\$

Calculate the exponents.

\$\Rightarrow CD = \sqrt{\frac{2(169) + 2(36) - 225}{4}}\$

Multiply.

\$\Rightarrow CD = \sqrt{\frac{338 + 72 - 225}{4}}\$

Add and subtract.

\$\Rightarrow CD = \sqrt{\frac{185}{4}}\$

Simplify.

\$Rightarrow CD = \frac{\sqrt{185}}{2}\$

Answer

The value of the median CD of triangle ABC = \$\frac{\sqrt{185}}{2}\$.