Question

Given that the two triangles below have a scale factor of 2:5, determine the perimeter of the larger triangle. Smaller sides of the triangle are 10,8,16.

Option 1: 80
Option 2: 40
Option 3: 32
Option 4: 64

Answer 1

To find the perimeter of the larger triangle when the scale factor is 2:5, multiply each side of the smaller triangle by 5/2, then sum the results. The perimeter of the larger triangle, calculated from the sides 10, 8, and 16 of the smaller triangle, is 85, which does not match any of the given options.

The correct answer is none of all.

Step-by-step explanation:

To determine the perimeter of the larger triangle with a given scale factor of 2:5, we follow these steps:

1. First, understand that all sides of the larger triangle will be scaled up by the same scale factor.
2. Calculate the lengths of the larger triangle's sides by multiplying the smaller triangle's sides by the scale factor (5/2).
3. For the smaller triangle with sides 10, 8, and 16, the scaled up sides will be 25, 20, and 40 respectively.
4. Finally, sum up these sides to obtain the perimeter of the larger triangle: 25 + 20 + 40 = 85.

Therefore, the perimeter of the larger triangle is 85, which is not provided in the given options.