Question

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

Answer 1

Formula of square area
a = s²
thus, area of the first square could be written as s₁² and area of the second square could be written as s₂²

First, write an expression in the form of equation system
An expression for "The combined area of two squares is 45 square centimeters" is:
⇒ s₁² + s₂² = 45 (first equation)
An expression for "Each side of one square is twice as long as side of the other" is:
⇒ s₁ = 2s₂ (second equation)

Second, solve the equation system by substitution method.
⇒ We could substitute 2s₂ to s₁ (second equation) in the first equation in order to find the value of s₂
s₁² + s₂² = 45
(2s₂)² + s₂² = 45
(2²)(s₂)² + s₂² = 45
4s₂² + s₂² = 45
5s₂² = 45
s₂² = 45/5
s₂² = 9
s₂² = 3²
s₂ = 3

⇒ Substitute the value of s₂ to the second equation in order to find the value of s₁
s₁ = 2s₂
s₁ = 2(3)
s₁ = 6

The length of each side of the larger square is 6 centimeters