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).

Question

Mathematics

Amos

28 February, 03:24

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).

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Answers (2)

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Anabelle Hernandez · Answer 1

Step-by-step 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)

Angela Stein · Answer 2

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)