You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
In a certain geometric diagram, a rectangle, a circle and a square are interconnected. The length of the rectangle is one fourth of the radius of the circle. The radius of the circle is equivalent to the side of a square, whose area is 784 sq. units. In the same diagram, a triangle is inscribed within the rectangle such that its base is equal to the *unknown* breadth of the rectangle and its height is equal to the known length of the rectangle. If the combined area of the rectangle and the inscribed triangle is 500 sq. units, what is the breadth of the rectangle?
user
47.62
rule
In a certain geometric diagram, a rectangle, a circle and a square are interconnected. The length of the rectangle is one fourth of the radius of the circle. The radius of the circle is equivalent to the side of a square, whose area is 784 sq. units. In the same diagram, a triangle is inscribed within the rectangle such that its base is equal to the *unknown* breadth of the rectangle and its height is equal to the known length of the rectangle. If the combined area of the rectangle and the inscribed triangle is 500 sq. units, what is the breadth of the rectangle?
train