Express the total area A enclosed by both squares (in sq.in.) in terms of x.

Question

A piece of wire 13 inches long is cut into two pieces and each piece is bent into a square. If x denotes the length (in inches) of the first piece, express the total area A enclosed by both squares (in sq.in.) in terms of x.

Answer 1

Hello Alexes,

 

First, we note that the wire is 13 inches long. Then if the first wired is  x in. long then the second wire is 13-x in. long.

Second, a square has four equal sides

 

............................................................................................................................................... 13 inches

 

wire1

----------------------------------------------  x inches                

 

 

wire2

--------------------------------------------------------------------- 13 - x inches

 

       x/4

------------            

|             |                                                                                                                                               

|             |   x/4                        Area of wire1 =  (x/4)*(x/4)         

------------    

 

   (13 - x)/4

---------------                  

|                |

|                |  (13 - x)/4             Area of wire2 = (13 - x)/4 * (13 - x)/4

|                |

---------------

 

Total area enclosed by both wires is = Area of wire1 + Area of wire2

 

                                                     = (x/4)² + [(13 - x)/4]²    

 

                                                     = x² /16 + [(169 - 26x +x²)/16]

 

                                                     = [x² + 169 - 26x +x²]/16

 

                                                     =[2x² - 26x +169]/16