Answer:
The dimensions are:
[tex]3(2x+1)[/tex] by [tex](7x+5)[/tex]
Step-by-step explanation:
The area of the rectangle is given as
[tex]A=42x^2+51x+15[/tex]
The factored form of this quadratic trinomial gives the dimensions of the rectangle.
We factor 3 first to obtain;
[tex]A=3(14x^2+17x+5)[/tex]
We split the middle term to get;
[tex]A=3(14x^2+10x+7x+5)[/tex]
We factor within the parenthesis to get;
[tex]A=3(2x(7x+5)+1(7x+5))[/tex]
We factor further to get;
[tex]A=3(2x+1)(7x+5)[/tex]
The dimensions are:
[tex]3(2x+1)[/tex] by [tex](7x+5)[/tex]
Then the perimeter will be
[tex]2(6x+3+7x+5)=26x+16\:\:\:\boxed{\sqrt{} }[/tex]
