Solving Triangle Ratios
The image shows two triangles with side lengths provided. The larger triangle has sides of length 21, 15, and 18, while the smaller triangle has one side labeled as 5 and two sides that are not labeled. It is stated that the ratio of the larger triangle to the smaller triangle is 3.
To solve the problem, we'll assume that the corresponding sides of the triangles are proportional, meaning that the larger triangle is a scaled-up version of the smaller one.
Since the ratio is 3, it implies that every length in the larger triangle is 3 times the length of the corresponding length in the smaller triangle.
The smaller triangle has a side with a length of 5. To find the corresponding side on the larger triangle, we can divide one of the side lengths of the larger triangle by 3. Let's choose the side length of 15 for simplicity:
15 (larger side length) / 5 (smaller side length) = 3
This confirms that the side length of 5 in the smaller triangle corresponds to the side length of 15 in the larger triangle.
To maintain the same scale, other sides of the smaller triangle should be 1/3 of their respective sides in the larger triangle.
Thus, the other two sides of the smaller triangle can be found by dividing the remaining sides of the larger triangle by 3:
21 / 3 = 7
18 / 3 = 6
So the smaller triangle should have side lengths of 5, 7, and 6.
However, since your question doesn't specify what needs to be solved, but only provides the ratio and the sizes of the triangles, I've provided you with the calculation that confirms the given ratio and the side lengths of the smaller triangle based on that ratio. If there's a specific question or calculation you need beyond this, please provide that information.
