Steps for solving Quadratic application problems:

1. Draw and label a picture if necessary.

2. Define all of the variables.

3. Determine if there is a special formula needed. Substitute the given information into the equation.

4. Write the equation in standard form.

5. Factor.

6. Set each factor equal to 0. And solve the linear equation. Eliminate any unreasonable answers. (Hint: We can't have -5 ft. of carpet.)

7. Check your answers.

 

 Area of a rectangle and Landscaping/border/frame problems . 

Example 1:A vacant rectangular lot is being turned into a community vegetable garden measuring 8 meters by 12 meters. A path of uniform width is to surround garden. If the area of the lot is 140 square meters, find the width of the path surrounding the garden.

Step 1:Draw and label a picture if necessary.

 E1.gif

Step 2:Define all of the variables.

e2.gif  

Step 3:Determine if there is a special formula needed. Substitute the given information to the equation.

e3.gif  

Step 4:Write the equation in standard form.

e4.gif  

Step 5:Factor.

 e5.gif

 

Step 6:Set each factor equal to 0. And solve the linear equation. Eliminate any unreasonable answers.

e6.gif  

Step 7:Check your answers.

ck.png  

 

Example 2:Each side of a square is lengthened by 7 inches. The area of this new larger square is 81 square inches. Find the length of a side of the original square.

Step 1:Draw and label a picture if necessary.

 4504.gif

Step 2:Define all of the variables.

 39.gif

Step 3:Determine if there is a special formula needed. Substitute the given information to the equation.

40.gif  

Step 4:Write the equation in standard form.

41.gif  

Step 5:Factor.

 100.png

Step 6:Set each factor equal to 0. And solve the linear equation. Eliminate any unreasonable answers.

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Step 7:Check your answers.

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