marios living room has a length 6 feet wider than the width. the area of the living room is 280 square feet. what are the dimensions of his living room?

Question

This lesson is about completing the square.

Answer 1

Let:
  W = width
  L = length = W + 6
 
Area = LW = (W+6)(W) = 280
 
    W2 + 6W = 280           [expand]

                                            [find this: 6/2 = 3 and 3*3 = 9]
    W2 + 6W + 9 = 289         [add 9 to both sides to make perfect square]
     (W+3)(W+3) = 289   
        W + 3 = 17            [take square root of both sides[
          W = 14 feet               [subtract 3 from both sides]
 
   L = W+ 6 = 20 feet

Answer 2

Hi Bernard,

 

 

 marios living room has a length 6 feet wider than the width. the area of the living room is 280 square feet. what are the dimensions of his living room?
This lesson is about completing the square.

 

 

Let's define the dimensions.

 

Let w= the width of the room

let w+6=length of the room

 

Area of a rectangle is A=lw.

 

280=(w+6)w

 

280=w²+6w

 

now we need to add -280 to both sides

 

w²+6w-280=0

 

since the last term is negative, one of the factors must be negative and the other positive.

since the 2nd term is positive, the larger of the factors must be positive.

 

we need factors of -280 which sum 6

 

-2    140 no

-4    62   no

-10  28   -10+28=18 no, but getting closer

-14   20    -14+20=6  YES!

 

w²+6w-280=0

(w-14)(w+20)=0  using the zero product property we can set each factor to zero and solve

 

w-14=0          w+20=0

w=14              w=-20   Since you cannot have negative length, this solution is rejected!

 

So the width is 14 feet.

Then the length is w+6=14+6=20

 

ANSWER:  The width is 14 feet and the length is 20 feet.

 

Please note:  this quadratic was able to be easily factored.  We didn't have to complete the square.

 

 

we're finished