A square poster 2 feet less than the sides of a square sign. difference between their areas is 24 , find the lengths of the sides of the poster and the sign.

Question

This is for a class

Answer 1

Good evening, Diedreanna.

 

To solve this, draw two squares, one larger than the other.  

The larger square is square sign.

The smaller square is the square poster.

 

The larger square has sides of length "x", its area is   x²

 

The smaller square has sides of length "x-2", its area is   (x-2)²

 

The difference of the areas A_big-A_small = x² - (x-2)^{2 = 24}

 

x² - (x-2)² = 24

 

x² - (x² - 4x + 4) = 24

 

x² - x² +4x - 4 = 24

 

4x - 4 = 24

 

4x = 28

 

x = 7

 

So the square sign is 7 x 7 sq ft, the square poster is 5 x 5 sq ft