Chapter 8.1, Problem 23WE

To determine

To find the length of $MK$ if $LM=6\&JM=4$ in the triangle shown below.

  

Answer to Problem 23WE

  $MK=6$

Explanation of Solution

Given:

  $LM=6\&JM=4$

Concept used:

When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse.

Calculation:

In the given triangle,

  $\begin{array}{l}\frac{JM}{LM}=\frac{LM}{MK}\\ \Rightarrow \frac{4}{6}=\frac{4}{MK}\\ \Rightarrow MK=6\end{array}$