Chapter 8.1, Problem 22WE

To determine

To find the length of $JM$ if $LM=4\&MK=8$ in the triangle shown below.

  

Answer to Problem 22WE

  $JM=2$

Explanation of Solution

Given:

  $LM=4\&MK=8$

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,

  $\begin{array}{l}\frac{JM}{LM}=\frac{LM}{MK}\\ \Rightarrow \frac{JM}{4}=\frac{4}{8}\\ \Rightarrow JM=\frac{16}{8}\\ \Rightarrow JM=2\end{array}$