Answer:
The length of the line segment UV is 76 units
Step-by-step explanation:
In a triangle, the line segment joining the mid-points of two sides is parallel to the third side and equal to half its length
In Δ ONT
∵ U is the mid-point of ON
∵ V is the mid-point of TN
→ That means UV is joining the mid-points of two sides
∴ UV // OT
∴ UV = [tex]\frac{1}{2}[/tex] OT
∵ UV = 7x - 8
∵ OT = 12x + 8
∴ 7x - 8 = [tex]\frac{1}{2}[/tex] (12x + 8)
→ Multiply the bracket by [tex]\frac{1}{2}[/tex]
∵ [tex]\frac{1}{2}[/tex] (12x + 8) = [tex]\frac{1}{2}[/tex] (12x) + [tex]\frac{1}{2}[/tex] (8) = 6x + 4
∴ 7x - 8 = 6x + 4
→ Add 8 to both sides
∴ 7x - 8 + 8 = 6x + 4 + 8
∴ 7x = 6x + 12
→ Subtract 6x from both sides
∴ 7x - 6x = 6x - 6x + 12
∴ x = 12
→ Substitute the value of x in the expression of UV to find it
∵ UV = 7(12) - 8 = 84 - 8
∴ UV = 76
∴ The length of the line segment UV is 76 units
