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Q16.

Expert-verified

Geometry

Found in: Page 291

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

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

The required value of $x$ is,

$x = \sqrt{117}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

We have given a figure as shown below,

Step 2. Use Pythagorean Theorem concept.

From Pythagorean Theorem,

we know that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

The given triangle is right triangle.

Therefore,

$\begin{matrix} 6^{2} + 9^{2} = x^{2} \\ 36 + 81 = x^{2} \\ 117 = x^{2} \end{matrix}$

Step 3. Taking square root.

we get,

$x = \pm \sqrt{117}$

Step 4. Neglect negative sign.

Since, square root is positive quantity

So, we neglect negative sign.

The required value of $x$ is, $x = \sqrt{117}$ .

Most popular questions for Math Textbooks

Given: $P Q R S$ is a rectangle.

$∠ A$ is a right angle.

Prove: $B S \cdot R C = P S \cdot Q R = {(P S)}^{2}$

Find the value of $x$ from the given figure.

Use the diagram to complete each statement..

$\begin{array}{l} I f m ∠ R = 30, t h e n m ∠ R S U = ?, \\ m ∠ T S U = ?, a n d m ∠ T = ? \end{array}$

Find the values of $x, y,$ and $z$ .

Simplify

$7 \sqrt{63}$

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