Answer:
8ft x 6ft
Step-by-step explanation:
For this problem, we want to create measurements of length and width that double our current area. First we need to find the current area.
C_Length = 6 ft
C_Width = 4 ft
C_Area = C_Length * C_Width
C_Area = 6 ft * 4 ft = 24 ft^2
Now we want our new area to be double the old area.
N_Area = 2C_Area
N_Area = 2 * 24 ft^2
N_Area = 48 ft^2
Now we simply need to find the increase in width and length, distributed equally, that will create the new area.
N_Area = (C_Length + x) * (C_Width + x)
Where x is the amount that each variable is increased by to create the new area.
Now we simply solve for x.
N_Area = (C_Length + x) * (C_Width + x)
48 = (6 + x) * (4 + x)
48 = 24 + 10x + x^2
0 = -24 + 10x + x^2
Now we can either apply the quadratic formula or attempt to factor using the constant break down method.
(x + 12) (x - 2) = 0
x = -12; x = 2
Note that we will choose x = 2 since the other option would require us to have negative material, which is impossible.
Now we can check to validate our answer by plugging in the value of x.
48 ?= (6 + 2) * (4 + 2)
48 ?= (8) * (6)
48 == 48
Thus, we have found the dimensions of the new aquarium, 8ft x 6ft.
Cheers.
