Question

the floor of a shed has an area of 96 square feet. the floor is in the shape of a rectangle whose length is 4 feet less than twice the width. find the length and the width of the floor of the shed.

Answer 1

To find the length and width of the floor of the shed, set up and solve the quadratic equation w * (2w - 4) = 96.

Step-by-step explanation:

1. Let's assume the width of the floor of the shed as 'w' feet.
2. According to the problem, the length of the floor is 4 feet less than twice the width. So, the length would be (2w - 4) feet.
3. Since the area of the floor is given as 96 square feet, we can set up the equation: w * (2w - 4) = 96.
4. Solve the quadratic equation to find the value of 'w' which represents the width of the floor.
5. Once you find the value of 'w', substitute it back into the equation (2w - 4) to find the length of the floor.

Answer 2

Alright in this one, you are going to need to factor.
The width is x
The length is 2x-4
To find the area of a rectangle is L*W
so (2x-4)(x) when distributed is 2x^2 -4x

Then put that in the equation and you have:
2x^2 -4x = 96
2x^2 -4x -96 = 0

2x^2+12x-16x-96=0
3x(x+4)-4(x+4)=0
(3x-4)=0
(x+4)=0
x=-4
x=3/4
Since length isn't negative
we will use 3/4 as x.

Width= 0.75 ft
Length= 1.5