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?
Accepted Solution
A:
Answer:The area of remaining wall after the mural has been painted is [tex]46x^2+73x+15[/tex] square units.Step-by-step explanation:If the dimensions of a rectangle are l and w, then area of rectangle is[tex]A=l\times w[/tex]The dimensions of wall are (6x+7) and (8x+5). So, the area of wall is[tex]A_1=(6x+7)\times (8x+5)[/tex][tex]A_1=6x(8x+5)+7(8x+5)[/tex][tex]A_1=48x^2+30x+56x+35[/tex][tex]A_1=48x^2+86x+35[/tex]The dimensions of mural are (x+4) and (2x+5). So, the area of mural is[tex]A_2=(x+4)\times (2x+5)[/tex][tex]A_2=x(2x+5)+4(2x+5)[/tex][tex]A_2=2x^2+5x+8x+20[/tex][tex]A_2=2x^2+13x+20[/tex]The area of remaining wall after the mural has been painted is[tex]A=A_1-A_2[/tex][tex]A=48x^2+86x+35-(2x^2+13x+20)[/tex][tex]A=48x^2+86x+35-2x^2-13x-20[/tex][tex]A=46x^2+73x+15[/tex]Therefore area of remaining wall after the mural has been painted is [tex]46x^2+73x+15[/tex] square units.