How do you find the radius of two circles inside a rectangle if the area of it is 50cm squared?

1 Answer
Oct 17, 2016

#r = 2.5cm#


I think a bit more detail is required about the the 2 circles? Are they equal in size and how are they placed?

I am going to assume that the two circles are equal in size and are side by side and fit exactly into the rectangle which has an area of #50 cm^2#

If you sketch the diagram and draw in the diameters of the circles so that they form a line through the middle of the rectangle, you will realise that the length of the rectangle is actually 4 radii.
In the same way, the breadth of the rectangle is 2radii.

So, we now know the length and the breadth of the rectangle, in terms of #r#, which is quite nifty because that is what we need to calculate. Form an equation for the area of the rectangle.

#l xx b = A#
# 4r xx 2r = 50#

#8r^2 = 50#

#r^2 = 50/8#

#r^2 = 6.25#

#r = sqrt6.25" "larr# only use the positive root

#r = 2.5cm#