Question 1

The perimeter of the larger triangle is 29.4.

The perimeter of the larger triangle is 29.4, which can be calculated based on the properties of similar triangles and the given dimensions.

A) 27.6

This option is incorrect as it does not reflect the proportionality of the sides of the similar triangles. The calculation based on the ratio of corresponding sides would yield a larger value than 27.6 for the perimeter of the larger triangle.

B) 28

While this option is close, it is still incorrect. The perimeter calculated from the similar triangles should account for the correct scaling factor, leading to a perimeter that exceeds 28.

C) 28.8

This option is also incorrect. Although it is a possible perimeter value, it does not align with the scaling factor derived from the dimensions of the triangles, which dictates a larger perimeter value.

D) 29.4

This is the correct answer because it accurately reflects the calculated perimeter of the larger triangle based on the given dimensions and the properties of similar triangles. The scaling factor applied to the smaller triangle's perimeter leads to this value.

E) 30.1

This option is incorrect as it exceeds the calculated perimeter for the larger triangle. Given the proportional relationship of the similar triangles, the perimeter cannot be this high.

Conclusion

The correct perimeter of the larger triangle is definitively 29.4, as it is derived from the proportionality of the similar triangles in question. All other options fail to meet the criteria set by the dimensions and ratios, thus confirming that D is the accurate answer.