A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 32 square feet. Find the lengths of the sides of the poster and the sign?
Area of square one = [tex](x-2)(x-2)[/tex] = [tex]x^2-4x+4[/tex] Area of square two = [tex]x^2[/tex]
The difference of the area of two squares = 32 [tex]x^2-(x^2-4x+4)=32[/tex] [tex]x^2-x^2+4x-4=32[/tex] [tex]4x-4=32[/tex] [tex]4x=32+4[/tex] [tex]4x=36[/tex] [tex]x=36/4[/tex] [tex]x=9[/tex]
The side length of the poster = [tex]x-2 = 9-2 = 7 feet[/tex] The side length of the sign = [tex]x=9[/tex]
