Answer:
[tex]Perimeter=54ft^2[/tex]
Step-by-step explanation:
Let's start by writing what we know in mathematical terms.
A rectangle has a length that is 3 more than twice its width, means:
[tex]L-3 = 2W\\L*W = 152[/tex]
Now all we have to do is solve for one of these values. I'll choose W.
Rewrite the equation:
[tex]L = 2W + 3[/tex]
Input that information into our second equation and solve:
[tex]W*(2W + 3) = 152\\2W^2+3W=152\\2W^2+3W-152=0[/tex]
Find the two W values by factoring the equation (note that the Width can't be negative because you can't have a negative rectangle):
[tex]2W^2+3W-152=0\\(2W+19)(W-8)=0\\\\W=-\frac{19}{2}\\W=8[/tex]
We pick the positive value 8 and plug it into our original equation to find Length:
[tex]L = 2W + 3\\L=2(8)+3\\L=19[/tex]
Finally, after all that, we can use the formula of a perimeter using our newly found Length and Width values (remember not to forget "ft^2" when we get our answer):
[tex]2L+2W\\2(19)+2(8)\\Perimeter=54ft^2[/tex]
