Question

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

Answer 1

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

Explanation:

`"Given : " bar(AC) = bar (BC) = 18, AB = 6, " To find median " bar(CD)`

`Delta ABC " is an isosceles triangle with " bar(CD) " perpendicular bisector of " bar(AB)`

Applying Pythagoras theorem,

`bar(CD) = sqrt ((AC)^2 - (AD)^2)`

`bar(AD) = bar(AB) / 2 = 6 / 2 = 3`

`bar(CD) = sqrt(18^2 - 3^2) ~~ 17.75`