For Sophia's graduation party, several tables of the same width will be arranged end to end to form a serving table with a
1 answer:
Answer:
Width=4.7 ft
Length=16.1 ft
Step-by-step explanation:
Let the width of the table to be x ft
Then the length should be two more than three times the width= 2+3x ft
The area of the serving table should be 75 ft²
But you know the area of this table is calculated by multiplying the length by the width of the table
Hence, Area= length× width
Length=x ft and width =2+3x ft
75ft²= (x ft) × (2+3x ft)
Apply the quadratic formula to solve this quadratic equation
The formula is ;
x= (-b ±√b²-4ac)÷2ac
where a=3, b=2 and c=-75
x= (-2 ± √2²-4×3×-75)÷(2×3)
x=(-2±√4+900)÷6
x=(-2±√904)÷6
x=(-2±30.1)÷6
x=(-2+30.1)÷6=4.683⇒4.7(nearest tenth)
or
x=(-2-30.1)÷6= -32.1÷6=-5.35⇒ -5.4
Taking the positive value
x=width =4.7 ft
2+3x= length= 2+3(4.7)=16.1 ft
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We have no dimensions to work with. I'll pick some and try and comply with the conditions of the problem.
Suppose you have an object that is 14 by 22 by 27 cm. These three numbers have no common factor so they cannot be reduced any further, which is helpful for this problem.
Find the Volume
Volume
l = 27 cm
w = 14 cm
h = 22 cm
V = 27 *14 * 22
V = 8316 cm^3
Find the surface area
SA = 2*l*w + 2*l*h + 2*w*h
SA = 2*27*14 + 2*27*22 + 2*14*22
SA = 756 + 1188 + 616
SA = 2558
Just looking at these numbers The surface area is about 1/3 of the volume. I don't think this is always true.
Another way to do this is to consider a cube which might give you a more useful result.
s = L = W = H all three dimensions are equal in a cube.
The volume of a cube is s*s*s = s^3
The surface area of a cube is 2*s*s + 2*s*s + 2s*s = 6s^2
That means whatever the side length, the Surface Area to volume = 6/the side length which is kind of an interesting result.
Suppose you have an object that is 14 by 22 by 27 cm. These three numbers have no common factor so they cannot be reduced any further, which is helpful for this problem.
Find the Volume
Volume
l = 27 cm
w = 14 cm
h = 22 cm
V = 27 *14 * 22
V = 8316 cm^3
Find the surface area
SA = 2*l*w + 2*l*h + 2*w*h
SA = 2*27*14 + 2*27*22 + 2*14*22
SA = 756 + 1188 + 616
SA = 2558
Just looking at these numbers The surface area is about 1/3 of the volume. I don't think this is always true.
Another way to do this is to consider a cube which might give you a more useful result.
s = L = W = H all three dimensions are equal in a cube.
The volume of a cube is s*s*s = s^3
The surface area of a cube is 2*s*s + 2*s*s + 2s*s = 6s^2
That means whatever the side length, the Surface Area to volume = 6/the side length which is kind of an interesting result.