Answer:
x = 8
Step-by-step explanation:
In the given triangle
- A line segment joining points on two sides and parallel to the 3rd side
- That means this line segment divided the two sides into equal ratios
- It divided the 1st side into 10 and 3x + 1
- It divided the 2nd side into 22 and 7x - 1
- 10/3x+1 = 22/7x-1
- By using cross multiplication
- 10(7x - 1) = 22(3x + 1)
- 10(7x) - 10(1) = 22(3x) + 22(1)
- 70x - 10 = 66x + 22
- Subtract 66x from both sides
- 70x - 66x - 10 = 66x - 66x + 22
- 4x - 10 = 22
- Add 10 to both sides
- 4x - 10 + 10 = 22 + 10
- 4x = 32
- Divide both sides by 4
- x = 8