15. Jenny has a triangular flag that has two sides 18 inches long and one side 6 inches long. She is making another triangular flag with angles equal in measure to the angles of the flag she has. If the new flag will have two sides 21 inches long, what will be the length of the third side?
Answer: A
The length of the third side will be 7 inches.
Given the relationship of the sides in similar triangles, if Jenny's new flag has two sides measuring 21 inches each, the proportionality can be applied to find the length of the third side.
A) 7 inches
This option is correct because the original flag has sides of lengths 18, 18, and 6 inches. The ratio of the sides of the new flag to the original flag is 21/18, which is 7/6. By applying this ratio to the third side of the original flag (6 inches), we get (6 inches * 7/6) = 7 inches.
B) 8 inches
This option is incorrect. If we were to set the third side as 8 inches, the proportionality from the original triangle would not hold true, as it does not maintain the same ratio compared to the other sides.
C) 9 inches
This option is also incorrect. A third side of 9 inches would imply a different ratio that does not match the scaling from the original triangle. It fails to satisfy the proportionality derived from the original flag's dimensions.
D) 10 inches
This option is incorrect as well. A third side of 10 inches would further deviate from the necessary proportionality based on the original dimensions, which requires maintaining the similar triangle aspect ratio.
Conclusion
The correct answer is definitively 7 inches, as it maintains the necessary proportional relationships of the sides in similar triangles. All other options fail to meet the criteria established by the original flag's dimensions, rendering them incorrect. Thus, 7 inches is the only viable answer based on the established ratios.