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Below is the transcription and explanation of the image as it would appear on an educational website: --- ### Understanding the Right Triangle In this exercise, we are given a right triangle with the following measurements: - One leg of the triangle is 3 units. - The other leg of the triangle (the base) is 9 units. - The hypotenuse (the side opposite the right angle) is labeled as \( x \). **Objective:** Find the length of the hypotenuse \( x \). #### Diagram Details: The image shows a right triangle with: - A vertical side measuring 3 units. - A horizontal base measuring 9 units. - A hypotenuse which is denoted by \( x \). To solve for \( x \), we use the Pythagorean theorem which states: \[ a^2 + b^2 = c^2 \] Here, \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse. Substituting the given values: \[ 3^2 + 9^2 = x^2 \] \[ 9 + 81 = x^2 \] \[ 90 = x^2 \] \[ x = \sqrt{90} \] Simplifying \( \sqrt{90} \): \[ x = 3\sqrt{10} \] Therefore, the length of the hypotenuse \( x \) is \( 3\sqrt{10} \). --- **Note:** The work under the image box confirms this result by showing the simplified form, indicating that \( x = 3\sqrt{10} \). This diagram and the associated problem help in understanding the practical application of the Pythagorean theorem in finding the hypotenuse of a right triangle. --- By presenting it this way, students can clearly follow the steps required to solve the problem and understand the application of the Pythagorean theorem.

Below is the transcription and explanation of the image as it would appear on an educational website: --- ### Understanding the Right Triangle In this exercise, we are given a right triangle with the following measurements: - One leg of the triangle is 3 units. - The other leg of the triangle (the base) is 9 units. - The hypotenuse (the side opposite the right angle) is labeled as \( x \). **Objective:** Find the length of the hypotenuse \( x \). #### Diagram Details: The image shows a right triangle with: - A vertical side measuring 3 units. - A horizontal base measuring 9 units. - A hypotenuse which is denoted by \( x \). To solve for \( x \), we use the Pythagorean theorem which states: \[ a^2 + b^2 = c^2 \] Here, \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse. Substituting the given values: \[ 3^2 + 9^2 = x^2 \] \[ 9 + 81 = x^2 \] \[ 90 = x^2 \] \[ x = \sqrt{90} \] Simplifying \( \sqrt{90} \): \[ x = 3\sqrt{10} \] Therefore, the length of the hypotenuse \( x \) is \( 3\sqrt{10} \). --- **Note:** The work under the image box confirms this result by showing the simplified form, indicating that \( x = 3\sqrt{10} \). This diagram and the associated problem help in understanding the practical application of the Pythagorean theorem in finding the hypotenuse of a right triangle. --- By presenting it this way, students can clearly follow the steps required to solve the problem and understand the application of the Pythagorean theorem.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Find the value of x

Below is the transcription and explanation of the image as it would appear on an educational website: --- ### Understanding the Right Triangle In this exercise, we are given a right triangle with the following measurements: - One leg of the triangle is 3 units. - The other leg of the triangle (the base) is 9 units. - The hypotenuse (the side opposite the right angle) is labeled as \( x \). **Objective:** Find the length of the hypotenuse \( x \). #### Diagram Details: The image shows a right triangle with: - A vertical side measuring 3 units. - A horizontal base measuring 9 units. - A hypotenuse which is denoted by \( x \). To solve for \( x \), we use the Pythagorean theorem which states: \[ a^2 + b^2 = c^2 \] Here, \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse. Substituting the given values: \[ 3^2 + 9^2 = x^2 \] \[ 9 + 81 = x^2 \] \[ 90 = x^2 \] \[ x = \sqrt{90} \] Simplifying \( \sqrt{90} \): \[ x = 3\sqrt{10} \] Therefore, the length of the hypotenuse \( x \) is \( 3\sqrt{10} \). --- **Note:** The work under the image box confirms this result by showing the simplified form, indicating that \( x = 3\sqrt{10} \). This diagram and the associated problem help in understanding the practical application of the Pythagorean theorem in finding the hypotenuse of a right triangle. --- By presenting it this way, students can clearly follow the steps required to solve the problem and understand the application of the Pythagorean theorem.
Transcribed Image Text:Below is the transcription and explanation of the image as it would appear on an educational website: --- ### Understanding the Right Triangle In this exercise, we are given a right triangle with the following measurements: - One leg of the triangle is 3 units. - The other leg of the triangle (the base) is 9 units. - The hypotenuse (the side opposite the right angle) is labeled as \( x \). **Objective:** Find the length of the hypotenuse \( x \). #### Diagram Details: The image shows a right triangle with: - A vertical side measuring 3 units. - A horizontal base measuring 9 units. - A hypotenuse which is denoted by \( x \). To solve for \( x \), we use the Pythagorean theorem which states: \[ a^2 + b^2 = c^2 \] Here, \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse. Substituting the given values: \[ 3^2 + 9^2 = x^2 \] \[ 9 + 81 = x^2 \] \[ 90 = x^2 \] \[ x = \sqrt{90} \] Simplifying \( \sqrt{90} \): \[ x = 3\sqrt{10} \] Therefore, the length of the hypotenuse \( x \) is \( 3\sqrt{10} \). --- **Note:** The work under the image box confirms this result by showing the simplified form, indicating that \( x = 3\sqrt{10} \). This diagram and the associated problem help in understanding the practical application of the Pythagorean theorem in finding the hypotenuse of a right triangle. --- By presenting it this way, students can clearly follow the steps required to solve the problem and understand the application of the Pythagorean theorem.
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