The combined area of two squares is 45 square centimeters. Each side of one square is twice as long as a side of the other square. What is the length of each side of the larger square?

A - side of the square

a₁ - arm the small square

a ₂ - larger side of the square

2a ₁ = a₂ we put into the equation 2

(a₁) ² + (a₂) ² = 45cm²

2a₁ = a₂

(a₁) ² + (2a₁) ² = 45cm²

(a₁) ² + 4 (a₁) ² = 45cm²

5 (a₁) ² = 45cm²

(a₁) ² = 9cm²

a₁ = √ (9cm²) = 3cm

a₂ = 2a₁ = 2*3cm = 6cm

A₁ = (a₁) ² = (3cm) ² = 9cm²

A₂ = (a₂) ² = (6cm) ² = 36cm²

A₁ + A₂ = 9cm² + 36cm² = 45cm²