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
Let x be the length of a side of the smaller square.
Since the sides of the larger square are twice as long as the sides of the smaller square, the length of a side of the larger square is 2x.
The area of a square is given by the formula A = side^2.
So, the area of the smaller square is x^2 and the area of the larger square is (2x)^2 = 4x^2.
Given that the combined area of the two squares is 45 cm^2, we have:
x^2 + 4x^2 = 45
5x^2 = 45
x^2 = 9
Solving for x, we get x = 3.
Therefore, the length of each side of the larger square (2x) is 2(3) = 6 cm.