# Not so little x

Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?

Two circles are enclosed by a rectangle 12 units by *x*
units.

The distance between the centres of the two circles is
*x*/3 units.

How big is *x*?

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Congratulations to Matthew Hodgetts, King Edward VI Camp Hill School, Birmingham, to Suzanne Abbott, Nisha Doshi and Christiane Eaves, Mount School, York; to Jessica Zhang; to the KS3 Maths Club, Strabane Grammar School and finally to Michael Swarbrick-Jones, Y7 Comberton Village College, Cambridge whose solution appears below.

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*x* = the diameter of one of the circles.

Since (AC) and (BD) are both the length of a radius then *x*
= (AC) + (BD).

So *x* = 12 - (AB) = 12 - *x*/3.

So *x* + *x*/3 = 12

or 4/3 *x* = 12.

To find *x* we take the reciprocal of 4/3 and multiply it
by 12.*x* = 9 units.