Question

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?

Answer 1

a - side of the square
a₁ - arm the small square
a₂ - larger side of the square
2a₁ = 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