Question

Samuel and his brother were playing soccer in the basement, and one particularly strong kick punctured a hole in the wall. The hole can almost be hidden by a 4 in. by 6 in. unframed picture, so Samuel thinks it will be completely hidden by the picture after it’s framed. Samuel hasn’t purchased the frame yet. Write a polynomial to represent the total area of the picture after it is framed. With the frame, the sides are (2x + 4) and (2x + 6).

Answer 1

The polynomial representing the total area of the picture after it is framed is
`4x^2 + 20x + 24`

Explanation:

The area of the frame can be found by using the area formula for the rectangle

we also have the sides of the framed picture

let (2x+6) be the length and (2x+4) be the width

Then area of the framed picture = length x breadth

On substituting the sides

Area of the framed picture =
`(2x+6) * (2x+4)`

Area of the framed picture =
`4x^2 +8x+ 12x + 24`

Area of the framed picture =
`4x^2 + 20x + 24`