Artist painting 400 square inch area

Question

An artist wants to frame a square painting with an area of 400 square inches. She wants to know the length of the wood trim that is needed to go around the painting.  a.) If x is the length of one side of the painting, what equation can you set up to find the length of a side? How many solutions does the equation have? b.) Do all of the solutions that you found make sense in the context of the problem? Explain. c.) What is the length of The wood trim needed to go around the painting?

Answer 1

The formula for the area of a square with sides of length x is  A = x²  so  

 

x² = 400  is the equation  

 

This equation has 2 solutions, namely x = ±√400 = +20 or -20  

 

The negative solution does not make sense because a length cannot be less than 0.  

 

The total length needed to go around the painting is the perimeter of the square, which is  

 

P = 4*x = 4*20 = 80 inches