Chapter 8.1, Problem 26WE

To determine

To find the length of $LJ$ if $JM=3\&MK=9$ in the triangle shown below.

  

Answer to Problem 26WE

  $LJ=6$

Explanation of Solution

Given:

  $JM=3\&MK=9$

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,

  $\begin{array}{l}\frac{JK}{LJ}=\frac{LJ}{JM}\\ \Rightarrow \frac{JM+MK}{LJ}=\frac{LJ}{3}\\ \Rightarrow \frac{3+9}{LJ}=\frac{LJ}{3}\\ \Rightarrow \frac{12}{LJ}=\frac{LJ}{3}\\ \Rightarrow {\left(LJ\right)}^2=36\\ \Rightarrow LJ=6\end{array}$