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35.0 cm (to 3 significant figures)

Step-by-step explanation:

Circumference of a circle = 2d (where d is the diameter).

Since the rectangle is inscribed in the circle (all 4 vertex touch, but not intersect, the circumference of the circle), we can see that the diameter of the circle is in fact the diagonal of the rectangle.

Therefore, to calculate the circumference we need to find the diagonal of the rectangle and plug it into the above formula.

To find the diagonal, we use Pythagoras' Theorem a² + b² = c²  (where a and b are the legs, and c is the hypotenuse of a right angled triangle).

From inspection, the diagram has given us the lengths of the legs as 9cm and 15cm.  So:  

 9² + 15² = c²

81 + 225 = c²

      306 = c²

             c = √306 = 3√34

Therefore, the diameter of the circle = 3√34 cm

Circumference = 2d

                         = 2 x 3√34

                         = 6√34

                         = 35.0 cm (to 3 significant figures)

answer: x=3 and y=4

step-by-step explanation: