Luke and Quinten are discussing what shapes the composite figure can be broken into. Luke wants to break it into four right triangles and one rectangle. Quinten wants to break it into two right triangles and two rectangles. Who identified a correct way to break up the shape?
To determine who identified a correct way to break up the shape, we need to consider the properties of the composite figure and how it can be divided into simpler shapes.
Luke wants to break the shape into four right triangles and one rectangle. This can be a valid approach if the composite figure contains four congruent right triangles that combine to form a rectangle. So, we need to check if the composite figure satisfies this condition.
On the other hand, Quinten wants to break the shape into two right triangles and two rectangles. This approach can also be valid if the composite figure can be divided in such a way that two congruent right triangles combine to form one rectangle, and the remaining parts also form one rectangle.
To determine if either approach is correct, we would need to visualize the composite figure and analyze its properties. It's difficult to provide a conclusive answer without a visual representation of the shape.
However, by comparing the two approaches, Luke's method of breaking the figure into four right triangles and one rectangle appears to be more likely to be correct. This is because breaking the figure into four congruent triangles and one rectangle is a simpler and more straightforward decomposition. Quinten's approach, involving two right triangles and two rectangles, might work for some composite figures, but it is generally less common and more complex.
It is important to note that without a visual representation of the composite figure, this analysis is based on assumptions and general principles. To make a definitive determination, it would be necessary to examine the specific composite figure in question.