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?

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?

oaktree · Answer

So let's call the length of the side of the shorter square x. That makes the length of the side of the longer one 2x. So the total area of the two squares is $$x^2 + (2x)^2 = 5x^2$$Which is equal to 45. So all you need to do is solve the equation $$5x^2=45$$which is the quadratic$$x^2=9$$Just square rooting both sides gives $$x=\pm3$$But since the length of a line segment must be positive, we know that x=3 must be the right choice. That makes the shorter square have side length 3, giving the longer one a side length of 6.

Let's double check our work. 
$$3^2 + 6^2 = 9+36=45$$So we're good!

anonymous · Answer

Thanks i can be so dumb sometimes.XD