Solve each problem. Check answers to be sure that they are...

Solve each problem. Check answers to be sure that they are reasonable. Refer to the formulas at the back of this text as needed. A square mirror has sides measuring 2 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. Check answers to be sure that they are reasonable. Refer to the formulas at the back of this text as needed.
A square mirror has sides measuring 2 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.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Area of a Square

This concept involves understanding that the area of a square is calculated by squaring the length of one of its sides. This formula is fundamental in geometry and is used to relate the side dimensions of a square to its overall area.

Setting Up Equations

In many problems, relationships between different quantities are expressed as equations. Here, the difference between the areas of two squares is set equal to a given value, which leads to the formation of an equation that can be solved for the unknown dimensions.

Expanding and Simplifying Expressions

When equations involve squared expressions, it is often necessary to expand these expressions and simplify the resulting equation. This step involves using algebraic identities, such as the square of a binomial, to combine like terms and isolate the variable.

Solving Linear Equations

After simplifying the expression obtained from the difference between the areas, the equation may reduce to a linear form. Solving linear equations involves isolating the variable by performing arithmetic operations, which provides the value of the unknown side lengths.

Transcript

Please give Ace some feedback