### Determining the Dimensions of a Pyramid Base#### The volume of a pyramid is given by the formula:\[ V = \frac{Bh}{3} \]where $ B $ is the area of its base and $ h $ is its height.#### Problem Statement:The volume of the given pyramid is 192 cubic centimeters. Find the dimensions of its rectangular base if one edge of the base is 2 centimeters longer than the other and the height of the pyramid is 12 centimeters.- **Volume ($ V $)**: 192 cm$^3$- **Height ($ h $)**: 12 cmFill in the blanks for the base dimensions:- __ cm (smaller value)- __ cm (larger value)---#### Detailed Diagram Explanation:The diagram below the text shows a rectangular-based pyramid. The key features labeled on the diagram include:- The height ($ h $) of the pyramid is shown with a vertical dashed line extending from the base to the apex of the pyramid.- The rectangular base has two dimensions: - $ x $ cm - $ x + 2 $ cmThe $ x $ value represents one edge of the rectangular base, while $ x + 2 $ represents the other edge which is 2 cm longer than the first. An arrow annotation labeled "2" shows the extra length added to $ x $ for the longer side. Given these details, the task is to solve for the values of $ x $ and $ x + 2 $.

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The volume of a pyramid is given by the formula V= Bh where B is the area of its base and h is its height. The volume of the following pyramid is 192 cubic centimeters. Find the dimensions of its rectangular base if one edge of the base is 2 centimeters longer than the other and the height of the pyramid is 12 centimeters. cm (smaller value) |cm (larger value)

The volume of a pyramid is given by the formula V= Bh where B is the area of its base and h is its height. The volume of the following pyramid is 192 cubic centimeters. Find the dimensions of its rectangular base if one edge of the base is 2 centimeters longer than the other and the height of the pyramid is 12 centimeters. cm (smaller value) |cm (larger value)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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### Determining the Dimensions of a Pyramid Base

#### The volume of a pyramid is given by the formula:
\[ V = \frac{Bh}{3} \]
where $ B $ is the area of its base and $ h $ is its height.

#### Problem Statement:
The volume of the given pyramid is 192 cubic centimeters. Find the dimensions of its rectangular base if one edge of the base is 2 centimeters longer than the other and the height of the pyramid is 12 centimeters.

- **Volume ($ V $)**: 192 cm$^3$
- **Height ($ h $)**: 12 cm

Fill in the blanks for the base dimensions:
- __ cm (smaller value)
- __ cm (larger value)

---

#### Detailed Diagram Explanation:
The diagram below the text shows a rectangular-based pyramid. The key features labeled on the diagram include:

- The height ($ h $) of the pyramid is shown with a vertical dashed line extending from the base to the apex of the pyramid.
- The rectangular base has two dimensions:
- $ x $ cm
- $ x + 2 $ cm

The $ x $ value represents one edge of the rectangular base, while $ x + 2 $ represents the other edge which is 2 cm longer than the first. An arrow annotation labeled "2" shows the extra length added to $ x $ for the longer side.

Given these details, the task is to solve for the values of $ x $ and $ x + 2 $.

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