An Egyptian Mummy stands upright in a case that is 3.5m high, and has a colume of 14m^3. The width of the case is half the length. What are the length and width of the case?
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Volume = L B H
but B = L/2
so
Volume = L (L/2) H
14 = L^2 * 3.5/2
L^2 = 28/3.5
take the square root
To find the length and width of the case, we need to use the given information that:
- The height of the case is 3.5m.
- The volume of the case is 14m².
- The width of the case is half the length.
Let's assign variables to the length and width:
- Let L represent the length of the case.
- Let W represent the width of the case.
From the given information, we can set up the following equations:
1. The volume of the case is given by the formula: Volume = Length × Width × Height. Therefore,
14 = L × W × 3.5 ----(Equation 1)
2. The width of the case is half the length. Therefore,
W = 0.5L ----(Equation 2)
To solve for L and W, we can substitute Equation 2 into Equation 1:
14 = (0.5L) × L × 3.5
14 = 1.75 L²
Next, we can isolate L by dividing both sides of the equation by 1.75:
L² = 14 ÷ 1.75
L² = 8
Taking the square root of both sides, we find:
L = √8 = 2.828...
However, the length cannot be negative, so we take the positive value:
L ≈ 2.828 m
Now we can substitute the value of L back into Equation 2 to find the width:
W = 0.5 × 2.828
W ≈ 1.414 m
Therefore, the length of the case is approximately 2.828 meters, and the width of the case is approximately 1.414 meters.
To find the length and width of the case, we can use the information given about its height and volume.
First, let's analyze the information given:
1. The height of the case is 3.5m.
2. The volume of the case is 14m^3.
3. The width of the case is half the length.
From the given information, we can set up a formula to find the length and width.
Volume of a rectangular box = length * width * height
Substituting the given values into the formula:
14m^3 = length * (length/2) * 3.5m
To simplify the equation, we can divide both sides by 3.5m:
4m = length^2/2
Now, multiply both sides of the equation by 2 to get rid of the fraction:
8m = length^2
To solve for the length, we take the square root of both sides:
√8m = √(length^2)
√8m = length
Therefore, the length of the case is approximately 2.83m.
Since the width of the case is half the length:
Width = length/2 = 2.83m/2 = 1.415m.
So, the length of the case is approximately 2.83m, and the width is approximately 1.415m.