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

Oct 17, 2016

$r = 2.5 c m$

Explanation:

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 $50 c {m}^{2}$

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.

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.

$l \times b = A$
$4 r \times 2 r = 50$

$8 {r}^{2} = 50$

${r}^{2} = \frac{50}{8}$

${r}^{2} = 6.25$

$r = \sqrt{6.25} \text{ } \leftarrow$ only use the positive root

$r = 2.5 c m$