A picture frame measures 12 cm by 20 cm, and 84 cm^2 of picture shows. Find the width of the fra

step 1 This question is asking us to find the width of a frame given the area of a picture frame the ar

A picture frame measures 12 cm by 20 cm, and 84 cm^2 of...

Key Concepts

Quadratic Equations

Often, the algebraic formulation in such frame problems leads to a quadratic equation. Solving quadratic equations, which can be done by factoring, completing the square, or using the quadratic formula, is a fundamental algebraic skill. This step is crucial for determining the dimensions or widths that satisfy the given conditions.

Geometric Modeling

This concept involves representing geometric figures and their elements, such as dimensions and borders, using variables. Instead of working with fixed numbers, the problem is abstracted into algebraic expressions that capture the relationships between the various parts of the figure. This approach is essential in solving problems where some quantities are unknown and need to be determined through forming and solving equations.

Area Calculation

The area of a rectangle is calculated by multiplying its length by its width. In these types of problems, understanding how to compute the area of both the overall figure and its inner region is crucial. This calculation allows one to relate the visible portion of the picture to the dimensions of the frame and the picture overall.

Algebraic Formulation

This key concept is about translating the geometric relationships into an algebraic equation. By setting up an equation that equates the expression for the inner area with a given value, the problem is transformed into an algebraic one that can be manipulated and solved for the unknown variable.

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