How to find length and width while given area

Question

The area of a rectangle is 80 square units. If the length is 6 less than 2 times the width, what is the perimeter? If someone could help me that would be great..!

Answer 1

Hi Abby

 

let width = w

so length = l= 2w -6

 

Area = length  * width

 

80  = (2w -6)(w)

 

80= 2w²-6w

 

2w²-6w-80 =0

 

divide by 2

 

w²-3w-40 =0

(w-8)(w+5) =0

w=8 or w =-5

 

width cannot be negative

 

w = 8 

 

width = 8 unit

length = 2(8)-6=16-6=10 unit

 

perimeter = 2(length +width) = 2(10 +8) =2(18)=36 unit

 

Answer 2

Hello, Abby,

The first thing you should do is underline key words and number.  2.  Then set up your information and draw a picture.

                A                =    80 sq. units                    L=    2w  -   6                      

The area of a rectangle is 80 square units.  If the length is 6 less than 2 times the width, what is the perimeter? 

 

__________

|_________|   w=width          Q:  What is the perimeter?    P=2l + 2w     We need to find the width first.

    l=2w-6

 

3.  Use the area formula to find the width.  They did give you the area as 80 sq. units.   A= L * W.

 

4.  Use substitution:  80= (2w-6)(w)       Quadratic equation   Use Distributive Property

 

5.  80= 2w² -6w                  You want to get zero on the right side of equation in order to factor.

                                            So, subtract -80 from both sides.

 

6  0=2w² -6w-80                 Simplify the entire equation by dividing every term by 2.

 

7.  0= w² -3w-40                  For example:    0/2       2/2       -6/2    and -80/2  

                                               Now, all you have to do  is factor.

 

8.  0=(w-8)(w+5)                  Set each factor equal to zero.

   0= (w-8)   or 0=(w+5)        0=(w-8)   Add +8 to both sides.    

 

     0=(w+5)    Get rid of 5 by subtracting it from both sides of equation.    

 

     8 =  w    or        -5=w          Now are lengths ever negative?  

 

 

Use w=8 to substitute into the length and to substitute into the perimeter equation.  I will let you finish your problem.

 

Thank you,

Susan C.

 

 

Answer 3

Hi, Abby.

 

w = width

l = 2w - 6

 

A = 80 = w(2w - 6)

2w² - 6w -80 = 0

 

w² - 3w - 40 = 0

 

(w - 8)(w + 5)  = 0

 

w = 8 , -5   (Since you can't have a negative length, w ≠ -5)

Therefore, w = 8

 

length = 2w - 6 = 10

 

So, 

length = 10 units

width = 8 units

 

So, the perimeter P = 2l + 2w = 2x10 + 2x8 = 20 + 16 = 36 units