Chapter 8.1, Problem 30WE

To determine

To find the length of $JM$ if $LK=7\&MK=6$ in the triangle shown below.

  

Answer to Problem 30WE

  $JM=\frac{13}{6}$

Explanation of Solution

Given:

  $LK=7\&MK=6$

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,

  $\begin{array}{l}\frac{JK}{LK}=\frac{LK}{MK}\\ \Rightarrow \frac{JM+MK}{7}=\frac{7}{6}\\ \Rightarrow JM+6=\frac{49}{6}\\ \Rightarrow JM=\frac{49}{6}-6\\ \Rightarrow JM=\frac{13}{6}\end{array}$