Chapter 8.1, Problem 29WE

To determine

To find the length of $JM$ if $LK=3\sqrt{6}\&MK=6$ in the triangle shown below.

  

Answer to Problem 29WE

  $JM=3$

Explanation of Solution

Given:

  $LK=3\sqrt{6}\&MK=6$

Concept used:

When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg.

Calculation:

In the given triangle,

  $\begin{array}{l}\frac{JK}{LK}=\frac{LK}{MK}\\ \Rightarrow \frac{JM+MK}{3\sqrt{6}}=\frac{3\sqrt{6}}{6}\\ \Rightarrow JM+6=\frac{54}{6}\\ \Rightarrow JM+6=9\\ \Rightarrow JM=3\end{array}$