Question

The outside of a rectangular picture frame has length 4x + 5 centimeters and width 2x + 3 centimeters. The picture window inside the frame is a rectangle that is 4x - 2 centimeters long and x + 1 centimeters wide.
a. Write a polynomial to describe the area (in square centimeters) of the picture window.
b. The picture frame, not including the window, is made of flat pieces of wood. Write a polynomial that describes the area (in square centimeters) of the wooden part of the frame. Explain your reasoning

Answer 1

The area of the wooden part of the frame is 4x² +20x +17 sq.cm , Area of a Rectangle is 4x² +2x-2 sq.cm .

What is a Rectangle ?

A rectangle is a polygon with four sides . The opposite sides are parallel and equal.

It is given that the outside length and breadth is 4x + 5 centimeters and width 2x + 3 centimeters.

inside the frame has length and breadth 4x - 2 centimeters long and x + 1 centimeters wide.

The polynomial to describe the area of the picture window

The dimension of the inner picture frame is the dimension of the picture window

Area of a Rectangle = Length *  Breadth

Area of a Rectangle = (4x-2) (x+1) = 4x² +4x -2x-2 = 4x² +2x-2 sq.cm

The picture frame area without the window =

Area of the total picture frame - Area of the inner picture frame

= (4x+5)(2x+3) - (4x-2)(x+1)

= 8x² + 12x +10x+15 -4x²-2x +2

= 4x² +20x +17

The area of the wooden part of the frame is 4x² +20x +17 .

To know more about Rectangle

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