Answer:
[tex]Perimeter = 45ft[/tex]
Step-by-step explanation:
Given
Represent the Length as L and the Width as W.
So, we have the following:
[tex]L = 2W + 3[/tex]
[tex]Area = 65[/tex]
Required
Determine the perimeter
The area of a rectangle is calculated as thus:
[tex]Area = L * W[/tex]
Substititute 65 for Area
[tex]65 = L * W[/tex]
Substitute 2W + 3 for L
[tex]65 = (2W + 3) * W[/tex]
This gives:
[tex]65 = 2W^2 + 3W[/tex]
Equate to 0
[tex]2W^2 + 3W - 65 = 0[/tex]
Expand:
[tex]2W^2 + 10W - 13W - 65 = 0[/tex]
Factorize:
[tex]2W(W + 5) - 13(W + 5) = 0[/tex]
[tex](2W - 13)(W + 5) = 0[/tex]
[tex]2W - 13 = 0\ or\ W + 5 = 0[/tex]
[tex]2W = 13\ or\ W = -5[/tex]
[tex]W = \frac{13}{2}[/tex] or [tex]W = -5[/tex]
But width can't be less than 0.
So:
[tex]W = \frac{13}{2}[/tex]
[tex]W = 6.5[/tex]
Recall that:
[tex]L = 2W + 3[/tex]
[tex]L = 2 * 6.5 + 3[/tex]
[tex]L = 16[/tex]
The perimeter is calculated as thus:
[tex]Perimeter = 2 * (L + W)[/tex]
[tex]Perimeter = 2 * (16 + 6.5)[/tex]
[tex]Perimeter = 45ft[/tex]
