Question

A group of art students are painting a mural on a wall. The rectangular dimensions of (6x+7) by (8x+5) and they are planning the mural to be (x+4) by (2x+5). What is the area of the remaining wall after the mural has been painted?

Answer 1

46x^2 + 73x + 15

Explanation:

Answer 2

The area of remaining wall after the mural has been painted is
`46x^2+73x+15` square units.

Explanation:

If the dimensions of a rectangle are l and w, then area of rectangle is

`A=l* w`

The dimensions of wall are (6x+7) and (8x+5). So, the area of wall is

`A_1=(6x+7)* (8x+5)`

`A_1=6x(8x+5)+7(8x+5)`

`A_1=48x^2+30x+56x+35`

`A_1=48x^2+86x+35`

The dimensions of mural are (x+4) and (2x+5). So, the area of mural is

`A_2=(x+4)* (2x+5)`

`A_2=x(2x+5)+4(2x+5)`

`A_2=2x^2+5x+8x+20`

`A_2=2x^2+13x+20`

The area of remaining wall after the mural has been painted is

`A=A_1-A_2`

`A=48x^2+86x+35-(2x^2+13x+20)`

`A=48x^2+86x+35-2x^2-13x-20`

`A=46x^2+73x+15`

Therefore area of remaining wall after the mural has been painted is
`46x^2+73x+15` square units.