Answer:the answer is 9.76 feet
Explanation:
A large chocolate bar has a base area of 61.56 square feet and its length is 0.6 feet shorter than twice its width. Find the length and the width of the bar
To find the length and width of the large chocolate bar, let's assign variables to the unknown values.
Let's say the width of the chocolate bar is represented by 'w' feet. According to the given information, the length of the chocolate bar is 0.6 feet shorter than twice its width. So, we can express the length as 2w - 0.6 feet.
The formula for the area of a rectangle is length multiplied by width. Given that the base area is 61.56 square feet, we can set up the equation:
w * (2w - 0.6) = 61.56
Now, let's solve this equation step by step:
1. Distribute the 'w' to the terms inside the parentheses:
2w^2 - 0.6w = 61.56
2. Rearrange the equation to set it equal to zero:
2w^2 - 0.6w - 61.56 = 0
3. To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula:
w = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 2, b = -0.6, and c = -61.56. Plugging these values into the quadratic formula, we get:
w = (-(-0.6) ± √((-0.6)^2 - 4 * 2 * (-61.56))) / (2 * 2)
Simplifying further:
w = (0.6 ± √(0.36 + 490.56)) / 4
w = (0.6 ± √490.92) / 4
4. Calculate the square root:
w ≈ (0.6 ± 22.14) / 4
This gives us two possible values for the width:
w1 ≈ (0.6 + 22.14) / 4 ≈ 5.18 feet
w2 ≈ (0.6 - 22.14) / 4 ≈ -5.135 feet
Since the width cannot be negative in this context, we discard the negative value.
5. Now, substitute the value of 'w' into the expression for the length:
Length = 2w - 0.6
Length ≈ 2 * 5.18 - 0.6
Length ≈ 10.36 - 0.6
Length ≈ 9.76 feet
Therefore, the width of the large chocolate bar is approximately 5.18 feet, and the length is approximately 9.76 feet.