Solve each problem. A square mirror has sides measuring 2 ft less than the sides of a square pai

Name: Problem 58, Chapter 5: Intermediate Algebra
Uploaded: 2022-02-25T20:46:29-08:00
Duration: 3 min 47 s
Channel: Rakshita Asati
Description: Solve each problem. A square mirror has sides measuring 2 ft less than the sides of a square painting. If the difference between their areas is 32 ft^2, find the lengths of the sides of the mirror and the painting.

step 1 Hello, so in this question we have been given a square mirror that has sides measuring two feet

Question

Solve each problem. A square mirror has sides measuring $2 \mathrm{ft}$ less than the sides of a square painting. If the difference between their areas is $32 \mathrm{ft}^{2}$, find the lengths of the sides of the mirror and the painting.

   Solve each problem.
A square mirror has sides measuring $2 \mathrm{ft}$ less than the sides of a square painting. If the difference between their areas is $32 \mathrm{ft}^{2}$, find the lengths of the sides of the mirror and the painting.

Intermediate Algebra

John Hornsby; Terry… 13th Edition

Chapter 5, Problem 58

Instant Answer

Solved by Expert Rakshita Asati

02/25/2022

Step 1

Therefore, the side of the mirror would be $x - 2$ (in feet), since it is given that the mirror's side is 2 feet less than the painting's side. Show more…

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Solve each problem. A square mirror has sides measuring $2 \mathrm{ft}$ less than the sides of a square painting. If the difference between their areas is $32 \mathrm{ft}^{2}$, find the lengths of the sides of the mirror and the painting.

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Key Concepts

Square Area Calculation

The area of a square is determined by squaring the length of its side. This concept is critical when dealing with problems that compare the areas of similar geometric figures, as it translates a linear dimension into a two-dimensional measure.

Algebraic Representation of Geometric Relationships

When comparing geometric shapes, it often becomes necessary to formulate the information given into algebraic equations. This involves assigning variables to unknown dimensions and using relationships (such as differences in size or area) to build equations that can be solved to find the unknowns.

Quadratic Equations

Many problems involving areas of geometric shapes lead to quadratic equations since the area of a square involves a squared term. Solving these equations typically requires expanding expressions, combining like terms, and applying methods such as factoring or using the quadratic formula to determine the values of the unknown variables.

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