Answer:
3 cm
Explanation:
The shaded area is the total area of the rectangle less the area of the unshaded square. The area of the rectangle is the product of its length and width:
A = (5x)·(3x) = 15x^2
Likewise, the area of the square is the product of its length and width:
a = (x)·(x) = x^2
Then the shaded area is the difference:
126 cm^2 = A -a = 15x^2 -x^2 = 14x^2
Dividing by 14 gives ...
9 cm^2 = x^2
and taking the square root tells us the value of x:
3 cm = x
This answers the question:
The side length of the square, x, is 3 cm.