Answer:
Length = 2w - 3
Length = 2(11.87) - 3
Length ≈ 20.74 ft
Step-by-step explanation: To find the length and width of the shed's floor, we can set up an equation based on the given information.
Let's assume the width of the floor is "w" feet. According to the question, the length is 3 feet less than twice the width, which means the length is (2w - 3) feet.
The area of a rectangle is calculated by multiplying the length by the width. In this case, we know that the area of the floor is 140 ft². Therefore, we can set up the equation:
w * (2w - 3) = 140
To solve this equation, we can expand and rearrange it:
2w² - 3w - 140 = 0
Now, we can factor the equation or use the quadratic formula to find the values of "w" that satisfy the equation. Factoring might not always be possible, so let's use the quadratic formula:
w = (-b ± √(b² - 4ac)) / 2a
For our equation, a = 2, b = -3, and c = -140. Plugging these values into the formula:
w = (-(-3) ± √((-3)² - 4(2)(-140))) / (2 * 2)
Simplifying further:
w = (3 ± √(9 + 1120)) / 4
w = (3 ± √1129) / 4
Using a calculator, we find two possible values for "w":
w ≈ 11.87 ft or w ≈ -5.37 ft
Since width cannot be negative, we disregard the negative value. Therefore, the width of the floor is approximately 11.87 ft.
Now, we can substitute the value of "w" back into the equation for the length:
Length = 2w - 3
Length = 2(11.87) - 3
Length ≈ 20.74 ft
Therefore, the length of the floor is approximately 20.74 ft and the width is approximately 11.87 ft.