To determine the approximate perimeter of the triangle when the angles are in the ratio 1:3.5 and the longest side measures 5 inches, follow these steps:
1. Understand the Scenario:
- The longest side of the triangle is given as 5 inches.
- The ratio of the side lengths is 1:3.5.
2. Calculate the Scale Factor:
- The length of the longest side (5 inches) corresponds to the side with the largest ratio value.
- The scale factor is obtained by dividing the longest side by the highest value in the ratio (3.5):
- Scale factor = 5 / 3.5
- Scale factor ≈ 1.4285714285714286
3. Determine the Lengths of the Other Sides:
- Using the scale factor, calculate the lengths of the other two sides:
- First side = 1 Scale factor
- First side ≈ 1.4285714285714286 inches
- Second side = 3.5 Scale factor
- Second side = 5 inches (which matches the given longest side, as expected because it was used to derive the scale factor)
4. Calculate the Perimeter:
- The perimeter of the triangle is the sum of all side lengths:
- Perimeter = First side + Second side + Longest side
- Perimeter ≈ 1.4285714285714286 + 5 + 5
- Perimeter ≈ 11.428571428571429 inches
Therefore, the approximate perimeter of the triangle is closest to 11.1 inches. Hence, the correct option is:
11.1 inches
