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Math 105: Precalculus Algebra14 chapters | 124 lessons | 12 flashcard sets

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Lesson Transcript

Instructor:
*Cathryn Jackson*

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Learning more about algebraic expressions and geometric figures will help you solve problems that occur in your life. In this lesson, you will use the perimeter of a two-dimensional geometric shape to solve a real-world problem.

I just bought this awesome new couch. I'm really excited because now I can host football parties at my house and invite all of my friends. The problem is, I don't know which wall in my living room my couch will fit on.

The living room and couch represent our first vocabulary word: **2-dimensional geometric figures**. 2-dimensional geometric figures are flat figures that have width and height. These figures can be drawn on a piece of paper; they do not have thickness. In this lesson, I am not evaluating the thickness of the couch or living room.

The **perimeter** of my living rooms is 50 feet, but I don't know the size of each wall, and I don't know how big the couch is. Perimeter is the distance all the way around an object. In this case, the perimeter of the living room is the length of all of the walls added together.

The long walls are 5*x* long, and the short walls are 2*x* + 4 long.

My couch is *x*^2 + 2 on the long sides and *x* width on the short sides.

I can find the lengths of the walls in my living room and the length and width of my couch by solving for *x*.

Remember, perimeter is the distance all the way around the object.

I know that the perimeter of my living room is 50 feet. I also know that the size of each of the long walls is 5*x*, and the short walls are 2*x* + 4. I can use the **algebraic expression** for each of the walls to find *x*. An **algebraic expression** is a math problem with at least one variable and no equal sign.

I am going to take each expression for each wall, add them together and make them equal to 50.

5*x* + 5*x* + (2*x* + 4) + (2*x* + 4) = 50

I can also use the **distributive property** to write my equation. The distributive property is multiplying an addition expression by multiplying each addend and then adding the product.

2(5*x*) + 2(2*x* + 4) = 50

Since I have two of each side, I can use the distributive property. Instead of adding 5*x* twice, I can multiply 5*x* by 2. Either way, you get the same answer:

10*x* + 4*x* + 8 = 50

Now, I'm going to add like terms:

14*x* + 8 = 50

Subtract 8 from each side of the equation to isolate the *x* variable:

14*x* = 42

Divide each side of the equation by 14 to isolate the *x* variable:*x* = 3

Now I can substitute 3 for *x* in the expressions to find the measurements of my walls and couch.

My long walls are 5*x*.

Substitute 3 for *x* and solve:

5(3)

My long walls are 15 feet long.

My short walls are 2*x* + 4.

Substitute 3 for *x* and solve:

2(3) + 4

My short walls are 10 feet long.

I can do the same thing with my couch.

The long side of my couch is *x*^2 + 2.

Substitute 3 for *x* and solve:

3^2 + 2

My couch is 11 feet long.

And since the width of my couch is *x*, and I know that *x* = 3, the width of my couch is 3 feet.

So, it looks like I'd better put my couch against one of the long walls in my living room, because it's just too long for my short walls.

In conclusion, you can solve algebraic expressions of any 2-dimensional shape by using the perimeter formula for each shape. The perimeter of a shape is the distance around the shape. By using algebraic expressions, you can figure out the length of the sides of any shape.

By the end of this lesson, you should be able to use the perimeter formula to create and solve an algebraic expression to find the lengths of the sides of a 2-D shape.

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Math 105: Precalculus Algebra14 chapters | 124 lessons | 12 flashcard sets

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