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user100 [1]
2 years ago
8

Find the length of line segment UV.

Mathematics
1 answer:
pshichka [43]2 years ago
8 0

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 = \frac{1}{2} OT

∵ UV = 7x - 8

∵ OT = 12x + 8

∴ 7x - 8 = \frac{1}{2} (12x + 8)

→ Multiply the bracket by \frac{1}{2}

∵ \frac{1}{2} (12x + 8) =  \frac{1}{2} (12x) +  \frac{1}{2} (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

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