SOLUTION: The length of the floor of a rectangular closet is 1 foot more than the width. The area of the floor is 56 square feet. Find the length and width of the floor. I figured the

Algebra ->  Rectangles -> SOLUTION: The length of the floor of a rectangular closet is 1 foot more than the width. The area of the floor is 56 square feet. Find the length and width of the floor. I figured the      Log On


   

Question 22221: The length of the floor of a rectangular closet is 1 foot more than the width. The area of the floor is 56 square feet. Find the length and width of the floor.

I figured the answer was 7 and 8, beacause it made sense. But how would I have algebraicly found that answer??
Found 2 solutions by queenofit, MORUPHOSUOLALE:
Answer by queenofit(120) About Me  (Show Source):
You can put this solution on YOUR website!
Length * Width = area
we know the length is 1 more than the width. so set it up like this
(L+1)(L)=56
multiply the left side
L^2+L=56
set this equal to zero
0=L^2 +L -56
use reverse foil to factor the equation
0= (x-7)(x+8)
set both values equal to zero
0=x-7 0=x+8
7=x -8=x
since you are dealing with lengths and widths you know that the answer cannot be a negative, so y is your width
w=7
w+1=length
7+1= 8
so you get the answer 7 and 8 as you assumed.

Answer by MORUPHOSUOLALE(24) About Me  (Show Source):
You can put this solution on YOUR website!

Area of the recatangular closet =
Area =LxW
56= LxW
SO IN OUR PROBLEM- LENGHT IS 1 FOOT MORE THAN THE WIDTH
SO, L= 1+W
WIDTH =W
OUR NEW DIMESION IS-

AREA= LENGHT X WINDTH
54=(1+W){W)
54=W(1+W}
54=W+W^2
0=W^2+W-54
REWRITE AS W^2+W-54=0 IN A QUADRATIC FORM.
TO SOLVE FOR W-
FACTORISE OR solving using Almighty quadratic fomulae to get the width
By factorizing-
(w+8)(w-7)=0
w=-8 or w=7
We will have to choose 7 ,because a width cannot be negative so,so the width is 7 feet.
Therefore if width is 7 feet.
Lenght=1+W
L=1+7
L=8
SO LENGHT= 8 FEET
WIDTH= 7 FEET
MORUPH OSUOLALE
CENTRAL PIEDMONT COLLEGE,
CHARLOTTE,NC