Finding an Algebraic Expression for the Perimeter of a Given Rectangle

Summary

Learn how to find the perimeter of a rectangle when its sides are represented by algebraic expressions. This video demonstrates two methods for adding up the sides and simplifying the resulting expression.

Highlights

Introduction to Perimeter with Algebraic Expressions00:00:01

The video begins by introducing the concept of finding the perimeter of a rectangle where the side lengths are given as algebraic expressions, specifically x + 4y and 2x + 3y. The goal is to add up all sides to find the perimeter.

Method 1: Adding All Four Sides Individually00:00:27

The first method shown is to directly add all four side lengths: (x + 4y) + (2x + 3y) + (x + 2y) + (2x + 3y). This involves summing each algebraic expression representing a side of the rectangle.

Method 2: Using the Formula 2*(length + width)00:00:57

A second, potentially easier method is presented, which uses the formula P = 2*(length) + 2*(width). In this case, it translates to 2*(x + 4y) + 2*(2x + 3y). It explains that both methods are correct.

Simplifying the Algebraic Expression00:01:28

The video then proceeds to simplify the expression obtained from the second method. It distributes the '2' into each set of parentheses: 2x + 8y + 4x + 6y. The next step is to combine like terms.

Combining Like Terms for the Final Perimeter00:01:42

The final step involves combining the 'x' terms (2x + 4x = 6x) and the 'y' terms (8y + 6y = 14y). The simplified algebraic expression for the perimeter is 6x + 14y, as 'x' and 'y' are not like terms and cannot be combined further.