A picture has a square frame that is 2 inches wide. The area...

Name: Problem 41, Chapter 5: Algebra 2
Uploaded: 2020-03-25T14:20:22-08:00
Duration: 1 min 55 s
Channel: Ankit Gupta
Description: A picture has a square frame that is 2 inches wide. The area of the picture is one third of the total area of the picture and frame. What are the dimensions of the picture to the nearest quarter of an inch?

A picture has a square frame that is 2 inches wide. The area of the picture is one third of the total area of the picture and frame. What are the dimensions of the picture to the nearest quarter of an inch?

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Key Concepts

Proportional Reasoning

Proportional reasoning involves understanding how one quantity relates to another by means of a ratio. In this problem, the fact that one area is a specific fraction of the total area forms the basis for setting up the relation between the picture's area and the overall area, leading to the necessary equation for finding dimensions.

Algebraic Equation Setup

Setting up algebraic equations is crucial for translating geometric relationships into solvable mathematical statements. By expressing the areas of different parts of a composite shape in terms of a variable and using given ratios, one can derive an equation that encapsulates the problem's conditions.

Square Geometry

This concept involves understanding that the area of a square is found by squaring its side length. It is fundamental when dealing with problems where dimensions and areas of squares are investigated, allowing one to relate linear dimensions to area measurements.

Composite Figures

Composite figures are shapes that consist of two or more simple geometric figures. In this context, a picture with a surrounding frame forms a composite figure, and analyzing its total area involves summing the areas of the distinct components or, equivalently, finding the difference between larger and inner shapes.

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