Will mark brainliest! Please help!A rectangle has a perimeter of (26x+16)cm and an area of (42x^2+51x+15)cm^2. Find the dimensions of the rectangle in terms of x.
Accepted Solution
A:
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]