Answer:
The value of x is 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
∴ [tex]\frac{10}{3x+1}[/tex] = [tex]\frac{22}{7x-1}[/tex]
→ 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
∴ The value of x is 8
