Question

Refer to the figure at the right.

If $JM=4$ and $JK=9$, find $LK$.

Short answer

The required valueis $LK=3\sqrt{5}$.

Step-by-step solution

Step 1. Given information.

In the given figure,

$JM=4 \& JK=9$

Step 2. 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.

Step 3. Find out the required value by using this concept.

In the given triangle,

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

Therefore, the required value is $LK=3\sqrt{5}$.