Answer :
Final answer:
To find the value of x, the sides of the given triangles suggest they may be similar, so we set up the proportion 15/17 = 7.5/x. We solve for x by cross-multiplying and dividing, finding x to be 8.5. The answer is confirmed as reasonable through logical checking, assuming the similarity.
Explanation:
To find x for the given triangles, we must first determine if the triangles are similar. If one triangle has sides of length 17 and 15, while the other has sides of length x and 7.5, we need to see if the sides are proportional because similar triangles have corresponding sides that are proportional. In this case, 7.5 is half of 15, which suggests that these two triangles could be similar. Assuming they are similar, we can set up the proportion 15/17 = 7.5/x.
Algebraically isolate the unknown quantity x by cross-multiplying to get 15x = 17 * 7.5. Simplify this to find x and we get x = (17 * 7.5) / 15, which simplifies to x = 8.5.
Finally, we check the answer to make sure it seems reasonable. Given that 7.5 is half of 15, it makes sense that x would be half of 17 if the triangles are indeed similar, and 8.5 is half of 17. This confirms that our calculated value for x is reasonable assuming similarity of the triangles.
