Name: ______Block: ___

FM 11 Completing the Square Word Problems 2

Example 1:

Farmer Mary has 12 m of fence and wants to build a rectangular pen.

In this example, length plus width must equal ______

List possible dimensions for her pen and calculate the areas for each. Include some dimensions that are not whole numbers.

Length / Width / Area = length x width

What do you think are the dimensions that will give Mary the largest area inside her pen?

What do you think are the dimensions that will give Mary the smallest area?

Example 1 with quadratic functions

Farmer Mary has 12 m of fence and wants to build a rectangular pen. Find the dimensions that give her maximum area in the pen.

Step 1 - Define your variables

y always equals area. x always equals the most plentiful side length. z is the other side length.

Step 2 - Make equations for area and total length.

Step 3 - Use substitution to make an equation with only x and y.

Step 4 - Complete the square and draw a graph. Find the dimensions that give maximum area.

Step 5 - Use a sentence and diagram to show the dimensions that give maximum area.

Example 2

Wandais going to make a pen with her 24 feet of fencing by making one side of the pen the side of her barn. Then she only needs to use her fencing on 3 sides. Find the dimensions that give her maximum area inside the pen.

barn

Step 1 - Define your variables

Step 2 - Make equations for area and total length.

Step 3 - Use substitution to make an equation with only x and y.

Step 4 - Complete the square and draw a graph. Find the dimensions that give maximum area.

Step 5 - Use a sentence and diagram to show the dimensions that give maximum area.

Practice

1. Jack wants to build a rectangular pen with 20 feet of fence. Find the dimensions that will maximize the area.

Step 1 - Define your variables

y always equals area. x always equals the most plentiful side length. z is the other side length.

Step 2 - Make equations for area and total length.

Step 3 - Use substitution to make an equation with only x and y.

Step 4 - Complete the square and draw a graph. Find the dimensions that give maximum area.

Step 5 - Use a sentence and diagram to show the dimensions that give maximum area.

2. Jack realizes can make a bigger pen if he uses his barn as one side of the fence. That way he only needs to use his 20 feet of fence to make 3 sides. Find the dimensions that will maximize the area in his pen.

barn

Step 1

Step 2

Step 3

Step 4

Step 5
3. Bernadette has 24 m of fence and wants to build 3 pens next to each other. Find the dimensions that will maximize the area.


4. Bernadette changes her mind and decides that she only needs 2 pens side by side from her 24 m of fencing. Find the dimensions that will maximize the area of these pens.


5. Bernadette changes her mind again and decides that she wants to make 4 pens from her 24 m of fencing. Find the dimensions that maximize the area.