91Ó°ÊÓ

A rectangle is a four-sided polygon with opposite sides that are equal in length and angles that are all right angles (90 degrees).
A rectangle is characterized by its length and width, which are the two dimensions necessary to calculate its area and perimeter.
These measurements form the basis for solving many algebraic problems related to geometry.
The properties of a rectangle make it a fundamental shape in various real-world applications.
Things to remember:

• Opposite sides are equal and parallel.
• The angles are all 90 degrees.
• The diagonals are equal in length and bisect each other.

Understanding these properties is essential for solving problems involving rectangles, such as calculating area, perimeter, and other quantities.

The area of a rectangle is a measure of the space it covers.
The formula to calculate the area is:
\( \text{Area} = \text{length} \times \text{width} \).
This formula helps us solve problems involving rectangles, like finding the missing length when the area and width are known.

Here’s how to use the formula:
1. Identify the length and width.
2. Multiply these two dimensions.
In our example, the area is given as 73.5 square yards, and the width is 3.5 yards. By rearranging the formula, we can solve for the length: \[ 73.5 = l \times 3.5 \]
To isolate the length (\( l \)), divide both sides by the width (3.5): \[ l = \frac{73.5}{3.5} \].
This calculation simplifies to give the length of the rectangle.

In algebra, a variable is a symbol, often a letter like \( l \) or \( x \), used to represent an unknown value.
Variables are essential in setting up and solving equations.

In our example, we let \( l \) represent the unknown length of the rectangle.
By expressing the known quantities (width and area) in terms of the variable, we can create an equation: \[ 73.5 = l \times 3.5 \].
Here's how to work with variables in such problems:

• Define the variable: Clearly state what the variable represents.
• Set up the equation: Use the given information to form an equation.
• Solve the equation: Perform algebraic operations to isolate the variable and find its value.

After defining the variable and setting up the equation, solving it involves basic arithmetic operations, like division in this case. The solution to the variable provides the unknown dimension, completing the problem.