Çözüldü Area of Square - Algebraic Identities (8th Grade)

Given constants x and y (where x > y) representing side lengths in centimeters, which are natural numbers, if the difference between their areas is 40 cm² and the difference between one of their side lengths is 4 cm, what is the sum of their areas in square centimeters?

x^2 - y^2 = 40
x - y = 4....(I)
(x - y)(x + y) = 40
4(x + y) = 40
x + y = 10....(II)
Summing the equations (I) and (II) side by side yields 2x = 14 ⇒ x = 7 cm....(III)
Substituting the value (III) for the equation (II), 7 + y = 10 ⇒ y = 3 cm....(IV)
Using the values (III) and (IV); 7^2 + 3^2 = 49 + 9 = 58 cm^2.

Source (Turkish): "8. Sınıf Bal Matematik Soru Bankası", Sayfa 185, Soru 8, Yanıtlar: Sayfa 331