Chapter 8.1, Problem 25WE

To determine

To find the length of $LK$ if $JM=4\&JK=9$ in the triangle shown below.

  

Answer to Problem 25WE

  $LK=3\sqrt{5}$

Explanation of Solution

Given:

  $JM=4\&JK=9$

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,

  $\begin{array}{l}\frac{JK}{LK}=\frac{LK}{MK}\\ \Rightarrow \frac{9}{LK}=\frac{LK}{JK-JM}\\ \Rightarrow \frac{9}{LK}=\frac{LK}{9-4}\\ \Rightarrow \frac{9}{LK}=\frac{LK}{5}\\ \Rightarrow {\left(LK\right)}^2=45\\ \Rightarrow LK=3\sqrt{5}\end{array}$