Algebra Application Example

 

Lets assume that the student asked what the solution to the below question.

 

Questions:

1.      For what values of m, does not have any real roots.

2.      If the area between the two triangles ABC and ADE shown in the diagram is 100 cm2, what is the value of r?

 

 

You can solve these questions by seeing the solutions to the given questions which use the same concepts

 


 

Questions which will help you to solve your question.

 

Question 1:  For what values of m, does not have any real roots.

 

 

Answer: A quadratic has real roots if the square root term in the quadratic formula is equal or greater than zero (Algebra Download).

 

If then the quadratic formula is written as . The quadratic has real roots if . In other words, the quadratic does not have any real roots .

 

In, ,  and , hence

 

                  

                  

                  

Squaring both sides gives

                  

                  

                  

That is

                    

or 

                  

 

Question 2: What is the area of the triangle shown below?

 

Answer: The area of a triangle is:

 

                  

                  

                  

                  

 

 

Question 3: If the area of the triangle is 7 unit2 , find the value of x.

 

Answer: The area of the triangle is , hence;

                  

                  

                  

                  

                         or     

                              or     

The answer must be positive, therefore .

 

Similarly by using the quadratic formula

                  

                  

                  

                       or        

The answer must be positive, hence .

 

Question 2: Find the length of DE, and the area of the triangle ADE.

 

Answer: Both angles at A are , i.e. are equal to each other. Therefore the triangles ABC and ADE are isosceles triangles and the height is a perpendicular bisector. The length of DE may be determined either using  or similar triangles.

 

                  

Using the triangle AHC,           

Using the triangle AFE,

Hence,