The floor of a shed has an area of 54 sq.feet. Find the length and
width if the length is 3 feet less than twice its width.
WL=54
W(2W-3)=54
2W^2-3W-54=0
(2W )(w )=0
(2W+9)(W-6)=0
w=6, L=9
To find the length and width of the shed's floor, we can set up a system of equations based on the given information.
Let's assume the width of the shed's floor is represented by 'w' feet.
According to the information given, the length of the floor is 3 feet less than twice its width. Therefore, the length can be represented as 2w - 3.
The area of the shed's floor is given as 54 sq.feet.
The formula for the area of a rectangle is length × width. So we have the equation:
length × width = 54
Substituting the expressions for length and width, we get:
(2w - 3) × w = 54
Expanding this equation, we have:
2w^2 - 3w = 54
To solve this quadratic equation, we can rearrange it into the form:
2w^2 - 3w - 54 = 0
Now, we can use factoring, completing the square, or the quadratic formula to solve for 'w'.