Given:
The area model.
The area of the shape is 82 square units.
To find:
The correct equation for the given situation.
Solution:
We know that, area of a rectangle is
[tex]Area=Length \times Width[/tex]
The figure is divided into 3 rectangles. Using this formula, the area of each rectangle is
[tex]A_1=(x)\times (3x)=3x^2[/tex]
[tex]A_2=(x)\times (4)=4x[/tex]
[tex]A_3=(3)\times (3x)=9x[/tex]
Now, the total area is equation to 82 square units.
[tex]A_1+A_2+A_3=82[/tex]
[tex]3x^2+4x+9x=82[/tex]
[tex]3x^2+13x=82[/tex]
Since the required equation is [tex]3x^2+13x=82[/tex], therefore, the correct option is C.
