Answer:
A rectangle is defined by its length = L, and its width = W.
So the perimeter of the of the rectangle can be written as:
Perimeter = 2*L + 2*W.
In this case, we want to leave the perimeter fixed, so we have:
24ft = 2*L + 2*W.
Now, we do not have any other restrictions, so to know the different dimensions now we can write this as a function, by isolating one of the variables.
2*L = 24ft - 2*W
L = 12ft - W.
or:
L(W) = 12ft - W.
Such that:
W must be greater than zero (because we can not have negative or zero width).
And W must be smaller than 12ft (because in that case we would have zero or negative length)
Then the possible different dimensions are given by:
L(W) = 12ft - W
0ft < W < 12ft.
For a single payment with compound interest, the equation to use is F=P(1+i)^n where F is the value after n periods, P is the present value, and i is the interest rate.
If we want the final value F to double in 5 years, F is then equal to P then n=5. The equation is now:
2P=P(1+i)^5
2=(1+i)^5
i=14.87% per year
