Question

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

Answer 1

Let $x$ be the side length of the small square. Then, the side length of the big square is $2x$.

The respective areas are $x^2$ and $(2x)^2=4x^2$

So, the sum of the areas are $x^2+4x^2=5x^2$

We have

$5x^2=45 \iff x^2=9 \iff x=\pm 3$

We can't have negative lengts, so we choose $x=3$

So, the side length of the larger square is 6.