Question

Two marbles are sitting side by side in a glass container.b the base of the container is 10 units long and the radius of the smaller marble is 2 units. What is the radius of the larger marble? Describe the strategy used to answer the question.

Answer 1

what does side-by-side mean?
touching?
both marbles touching a vertical line between them?

Do both marbles touch the (presumably vertical) sides of the container?

clearing up these questions will be a good place to start.

In the most reasonable scenario, marbles touching each other and the sides of the container, draw a diagram. If the radius of the larger is r, and the horizontal distance between the centers of the marbles is s,

r+s+2 = 10
(r-2)^2 + s^2 = (r+2)^2

to see this, consider the line joining the centers of the marbles.

so,

(r-2)^2 + (8-r)^2 = (r+2)^2
r = 4(3-√5) = 3.0557

Answer 2

Steve this makes sense to me. Thank you
I knowvitbis a lot to ask, but how do you get from
(r-2)^2 + (8-r)^2 = (+2)^2 to r=4(3-rt5)

Answer 3

I think he used the quadratic formula which is -b +/- rt (b^2 - 4ac) all that divided by 2a