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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 8: Q30. (page 288)

Refer to the figure at the right.
If $L K = 7$ and $M K = 6$ , find $J M$ .

Short Answer

Expert verified

The required valueis $J M = \frac{13}{6}$ .

Step by step solution

01

Step 1. Given information.

In the given figure,

$L K = 7 鈥� 鈥� & 鈥� 鈥� M K = 6$

02

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.

03

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

In the given triangle,

$\begin{matrix} \frac{J K}{L K} = \frac{L K}{M K} \\ \frac{J M + M K}{7} = \frac{7}{6} \\ J M + 6 = \frac{49}{6} \\ J M = \frac{49}{6} 鈭� 6 \\ J M = \frac{13}{6} \end{matrix}$

Therefore, the required valueis $J M = \frac{13}{6}$ .

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