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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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## Geometry Challenge

**Name:** __________

### Instructions:
Calculate the missing length (x) for each of the diagrams below.

### Diagram Description:
A four-sided polygon is depicted, consisting of a right triangle adjacent to a rectangle. The right triangle shares one side (with length 12) with the rectangle. The other sides of the polygon are marked as follows:

- The hypotenuse of the right triangle is labeled as 14.
- One side of the rectangle, perpendicular to the side shared with the triangle, is labeled 6.
- The length to be determined, x, is the vertical side of the right triangle.

### Task:
Apply the Pythagorean theorem to find the value of x. Use the relationship:   
\[ a^2 + b^2 = c^2 \]   
where:
- \( c = 14 \) (the hypotenuse),
- \( a = x \) (the unknown side),
- \( b = 12 \) (the known side of the right triangle).
Transcribed Image Text:## Geometry Challenge **Name:** __________ ### Instructions: Calculate the missing length (x) for each of the diagrams below. ### Diagram Description: A four-sided polygon is depicted, consisting of a right triangle adjacent to a rectangle. The right triangle shares one side (with length 12) with the rectangle. The other sides of the polygon are marked as follows: - The hypotenuse of the right triangle is labeled as 14. - One side of the rectangle, perpendicular to the side shared with the triangle, is labeled 6. - The length to be determined, x, is the vertical side of the right triangle. ### Task: Apply the Pythagorean theorem to find the value of x. Use the relationship: \[ a^2 + b^2 = c^2 \] where: - \( c = 14 \) (the hypotenuse), - \( a = x \) (the unknown side), - \( b = 12 \) (the known side of the right triangle).
**Right Triangle Challenge**

*Find the value of \(x\) in each of the diagrams.*

---

**Diagram Explanation:**

The image shows a shape that resembles a house with a pointed roof, divided into a right triangle on top and a rectangle below. The right triangle is on the top left side, with its height denoted as \(x\). The rectangle is below the triangle, with its height also labeled as \(x\) and its total height as 8 units.

To solve for \(x\), one could apply the Pythagorean theorem if needed, depending on additional information that is not visible in this text.
Transcribed Image Text:**Right Triangle Challenge** *Find the value of \(x\) in each of the diagrams.* --- **Diagram Explanation:** The image shows a shape that resembles a house with a pointed roof, divided into a right triangle on top and a rectangle below. The right triangle is on the top left side, with its height denoted as \(x\). The rectangle is below the triangle, with its height also labeled as \(x\) and its total height as 8 units. To solve for \(x\), one could apply the Pythagorean theorem if needed, depending on additional information that is not visible in this text.
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