polynomial for the sum of the areas of the rectangles

Question

Solve. (a) Find a polynomial for the sum of the areas of the rectangles: Length 8x, Width x, Length x, Width x (b). Length 3 Width x, Length x Width x: Find the sum of the area when x=3 and x=2. 3

Answer 1

The area is length × width.

 

a)  Length one = 8x

     Width one = x

     Length two = x

    Width two = x

 

A(x) = area of one rectangle + area of rectangle two

       = 8x * x  +  x * x

       = 8x² + x²

      = 9x²

 

 

b) Length one = 3

    Width one = x

    Length two = x

    Width two = x

 

A(x) = area of one rectangle + area of rectangle two

       = 3x + x²

       = x(3 + x)

 

Plug in the two x values separately to find the area.  I leave this part to you