Question

a rectangular picture is 6 centimeters longer than it is wide. A frame 1 cm wide is placed around the picture. Write a polynomial that represents the area of the frame.

Answer 1

Let the width of rectangular frame is x cm. It is given that the frame is 6 cm longer than it is wide. Therefore, the length of the frame will be (x + 6) cm.

A frame of 1 cm is placed all around the picture. This will increase the length and width of the frame from all four sides by 1 cm.

So, the new width will be (x + 2) cm and the new length will be (x +8) cm.

Area of rectangle = Length x Width

So, area of rectangular frame will be (x+2)(x+8) square centimeters.

Simplifying the expression we get:

Area =
`x^(2) +2x+8x+16`

Area =
`x^(2) +10x+16`

The above polynomial represents the Area of the frame.