Chapter 8.1, Problem 24WE

To determine

To find the length of $LM$ if $JM=3\&MK=6$ in the triangle shown below.

  

Answer to Problem 24WE

  $LM=3\sqrt{2}$

Explanation of Solution

Given:

  $JM=3\&MK=6$

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,

  $\begin{array}{l}\frac{JM}{LM}=\frac{LM}{MK}\\ \Rightarrow \frac{3}{LM}=\frac{LM}{6}\\ \Rightarrow {\left(LM\right)}^2=18\\ \Rightarrow LM=3\sqrt{2}\end{array}$