**Problem 8:**A picture frame is a rectangle that on the outside measures 32 cm by 40 cm and is of uniform thickness (distance of picture to outside edge of the frame). What is the thickness of the frame if 768 cm² of the picture shows? **Explanation:**To solve this problem, consider the dimensions of the entire frame and the dimensions of the picture. The outer dimensions of the frame are 32 cm by 40 cm. The area of the entire frame is 32 cm × 40 cm = 1280 cm².Since 768 cm² of the picture shows, the area of the picture is 768 cm². The difference in area (1280 cm² - 768 cm²) represents the area occupied by the frame itself.To find the thickness of the frame, let the thickness be $ t $. The inner dimensions of the picture are then $ (32 - 2t) $ and $ (40 - 2t) $ because the frame reduces the length and width each by twice the thickness.Set up the equation for the inner area:\[ (32 - 2t)(40 - 2t) = 768 \]Solving for $ t $ will give the thickness of the frame.

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8. A picture frame is a rectangle that on the outside measures 32 cm by 40 cm and is of uniform thickness (distance of picture to outside edge of the frame). What is the thickness of the frame if 768 cm? of the picture shows?

8. A picture frame is a rectangle that on the outside measures 32 cm by 40 cm and is of uniform thickness (distance of picture to outside edge of the frame). What is the thickness of the frame if 768 cm? of the picture shows?

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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Question

**Problem 8:**

A picture frame is a rectangle that on the outside measures 32 cm by 40 cm and is of uniform thickness (distance of picture to outside edge of the frame). What is the thickness of the frame if 768 cm² of the picture shows?

**Explanation:**

To solve this problem, consider the dimensions of the entire frame and the dimensions of the picture. The outer dimensions of the frame are 32 cm by 40 cm. The area of the entire frame is 32 cm × 40 cm = 1280 cm².

Since 768 cm² of the picture shows, the area of the picture is 768 cm². The difference in area (1280 cm² - 768 cm²) represents the area occupied by the frame itself.

To find the thickness of the frame, let the thickness be $ t $. The inner dimensions of the picture are then $ (32 - 2t) $ and $ (40 - 2t) $ because the frame reduces the length and width each by twice the thickness.

Set up the equation for the inner area:

\[ (32 - 2t)(40 - 2t) = 768 \]

Solving for $ t $ will give the thickness of the frame.

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