Question

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

Answer 1

`r = 2.5cm`

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 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`