Respuesta :
Perimeter of a rectangle = 6x + 8
Solution:
Given area of a rectangle = [tex]2x^2+7x+3[/tex]
Let us first factor the given polynomial.
[tex]2x^2+7x+3=2x^2+x+6x+3[/tex]
[tex]=(2x^2+x)+(6x+3)[/tex]
Taking out common terms in the above expression
[tex]=x(2x+1)+3(2x+1)[/tex]
Taking out common term [tex]2x+1[/tex] in the above expression
[tex]=(2x+1)(x+3)[/tex]
[tex]2x^2+7x+3=(2x+1)(x+3)[/tex]
Area of a rectangle = l × b
Therefore, [tex]l=2x+1[/tex] and [tex]b=x+3[/tex]
Perimeter of a rectangle = 2(l + b)
[tex]=2[(2x+1)+(x+3)][/tex]
[tex]=2(2x+1+x+3)[/tex]
[tex]=2(3x+4)[/tex]
[tex]=6x+8[/tex]
The answer is same if you take l = x + 3 and b = 2x + 1.
Hence, perimeter of a rectangle = 6x + 8.
