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?
Age
11 to 14
Challenge level
Problem
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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Student Solutions
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.