Area, Length, Width

Question

The area of a rectangular wall of a barn is 300 square feet. Its length is 10 feet longer than twice its width. Find the length and width of the wall of the barn.

Answer 1

Hello, Kay,

It might be a good idea to highlight key words and numbers in the story problem.    Let w= width

 

                           A= l*w                  A   =  300                   l   =    2w  +10

The area of a rectangular wall of a barn is 300 ft². Its length is 10 feet longer than twice its width. 

 

Q:  Find the length and the width of the wall of the barn.

 

2.  Use substitution:     A= L*W=               300= (2w+10) (1w)          Multiply using Distributive Property.

 

3.      300 =  2w² +10w        You have a Quadratic; write in standard form, (300=ax² + bx +c).

 

4.  0= 2w² +10w-300               Simplify by dividing every term by 2.

 

5.  0/2  = (2/2)w² + (10/2)w - (300/2)                0= w² + 5w - 150          

 

6.  Now, you may factor 0= (          )   (         )  , or you can use the Quadratic Equation to find "w."

 

7  I am going to let you finish your problem.       Susan C.