Two marbles are sitting side by side in a glass container. 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 you are going to use to answer the question.
no idea. What shape is the container? Do the marbles touch all of the nearest sides of the container? Only one side? Any sides at all?
Lots of specifics left out here.
To find the radius of the larger marble, we can use the concept of similar triangles. Here's the strategy we can use:
1. Visualize the scenario: Imagine the two marbles sitting side by side in the glass container with the smaller marble on the left and the larger marble on the right.
2. Identify the vertical line segments: Draw two vertical lines, one going through the center of each marble. These vertical lines will be the same length since the marbles are sitting side by side.
3. Set up a ratio: Determine the length of each vertical line segment. The vertical line segment for the larger marble will be the sum of the radius of the smaller marble (2 units) and the radius of the larger marble (unknown). The vertical line segment for the smaller marble will be twice the radius of the smaller marble.
4. Establish the ratio: Set up a ratio by dividing the vertical line segment for the larger marble by the vertical line segment for the smaller marble. This ratio will be equal to the ratio of the radius of the larger marble to the radius of the smaller marble.
5. Solve the equation: Substitute the given measurements into the ratio equation and solve for the radius of the larger marble.
By following these steps, we can find the radius of the larger marble.