I can’t figure this problem out

Question

The length of a rectangular garden is 5 m greater than the width. The area of the garden is 104 m² . Find the dimensions of the garden

Answer 1

Hello, Shelby,

Here is the model:       A=104 m²

__________

|                | w            A= l*w                             using substitution:     104 =(w+5) (w)  

|_________|

   l=w+5

                                                                      Multiply by using the Distributive Property:  104= w²+ 5w

 

Now, you want to write the Quadratic Equation ( 104=w²+5w) in standard form(0=ax²+bx+c).  By doing that, you will be able to factor or use the Quadratic Equation to find "w" and then, the length.

 

104-104= w² +5w -104                   0=w²+5w-104          0=(w-__)(w+__)

 

Note:  Only a positive width will work for this problem because there is no such thing as a negative length.

 

I will let you finish your problem.  Susan C     

Answer 2

L = W + 5

 

A = LW = (W + 5)W

 

104 = (W + 5)W = W² + 5W

 

W² + 5W - 104 = 0

 

(W - 8)(W + 13) = 0

 

W = 8 m

L = W + 5 = (8 + 5)m = 13 m