Find the length of the median of one of the legs of an isosceles triangle with sides the lengths 18,18,and 6?

Aug 11, 2018

color(maroon)("Length of the median " bar(CD) ~~ 17.75 " units"

Explanation:

$\text{Given : " bar(AC) = bar (BC) = 18, AB = 6, " To find median } \overline{C D}$

$\Delta A B C \text{ is an isosceles triangle with " bar(CD) " perpendicular bisector of } \overline{A B}$

Applying Pythagoras theorem,

$\overline{C D} = \sqrt{{\left(A C\right)}^{2} - {\left(A D\right)}^{2}}$

$\overline{A D} = \frac{\overline{A B}}{2} = \frac{6}{2} = 3$

$\overline{C D} = \sqrt{{18}^{2} - {3}^{2}} \approx 17.75$