Apiece of string 10 meters long is cut into two pieces to form two squares. if one piece of string has length x meters, show that the combined area of the two squares is given by a = 1/8( x^2 - 10x + 50 ).

Step-by-step explanation:

Length of 1 piece: x

Side of this square: x/4

Length of the second piece: 10 - x

Side of this square: (10 - x)/4

Combined area:

(x/4)² + [(10 - x)/4]²

x²/16 + (100 - 20x + x²)/16

[x² + 100 - 20x + x²]/16

[2x² - 20x + 100]/16

(x² - 10x + 50)/8

⅛(x² - 10x + 50)