Question

A piece 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 ).

Answer 1

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)

Answer 2

Explanation:

A = (x/4)^2 + ((10-x)/4)^2

A = x^2/16 + (10/4 - x/4)^2

A = x^2/16 + 100/16 - 2*10/4*x/4 + x^2/16

A = x^2/8 + 100/16 - 2*10/4*x/4

A = x^2/8 + 100/16 - 10/8*x

A = x^2/8 + 50/8 - 10/8*x

A = 1/8*(x^2 + 50 - 10*x)

A = 1/8*(x^2 - 10*x + 50)