Chapter 8.1, Problem 27WE

To determine

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

  

Answer to Problem 27WE

  $MK=9$

Explanation of Solution

Given:

  $JM=3\&JL=6$

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,

  $\begin{array}{l}\frac{JK}{JL}=\frac{JL}{JM}\\ \Rightarrow \frac{JM+MK}{6}=\frac{6}{3}\\ \Rightarrow 3+MK=12\\ \Rightarrow MK=9\end{array}$