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Q23.

Expert-verified

Geometry

Found in: Page 288

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

Refer to the figure at the right.
If $L M = 6$ and $J M = 4$ find $M K$ .

The required value is $M K = 6$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

In the given figure,

$L M = 6 & J M = 4$

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,

$\begin{matrix} \frac{J M}{L M} = \frac{L M}{M K} \\ \frac{4}{6} = \frac{4}{M K} \\ M K = 6 \end{matrix}$

Therefore, the required value is $M K = 6$ .

Most popular questions for Math Textbooks

The arithmetic mean between two numbers $r$ and $s$ is defined to be $\frac{r + s}{2}$ .

$(a) .$ $\bar{C M}$ is the median and $\bar{C H}$ is the altitude to the hypotenuse of right $Δ A B C$ . Show that $C M$ is the arithmetic mean between $A H$ and $B H$ , and that $C H$ is the geometric mean between $A H$ and $B H$ . Then use the diagram to show that the arithmetic mean is greater than the geometric mean.

$(b) .$ Show algebraically that the arithmetic mean between two different numbers $r$ and $s$ is greater than the geometric mean.

$(a) .$

Find the length of the diagonal of the square with perimeter is $16$ .

State an equation you could use to find the value of $x$ . Then find the value of $x$ in simplest radical form.

Simplify.

$\sqrt{75}$

Simplify.

$4 \sqrt{28}$

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