Respuesta :
Answer:
Option C is correct
[tex]l = x+4[/tex] unit and [tex]w = x+3[/tex] unit
Step-by-step explanation:
Area of a rectangle is given by:
[tex]A =lw[/tex] ....[1]
where
A is the area of rectangle
l is the length of a rectangle
w is the width of a rectangle.
As per the statement:
A certain rectangle has an area of [tex]x^2 + 7x + 12[/tex]
⇒[tex]A = x^2+7x+12[/tex]
Now factor this trinomial :
[tex]A = x^2+4x+3x+12[/tex]
⇒[tex]A = x(x+4)+3(x+4)[/tex]
⇒[tex]A=(x+4)(x+3)[/tex] unit square
On comparing with [1] we have;
[tex]l = x+4[/tex] unit and [tex]w = x+3[/tex] unit
Therefore,the length and width of the rectangle are:
[tex]l = x+4[/tex] unit and [tex]w = x+3[/tex] unit
