Question

TU || VX. Find UV.

63
45
15
V
W
T
X
U

Answer 1

21

Explanation :

To find UV, we can consider the side splitter theorem which states that when a line is parallel to a side of the triangle it passes through,it divides the two sides it touches into an equal proportion making UV/VW = TX/WX.

we are given that TW = 45 units and UW = 63 units moreover UV and VW together forms UW and TX and WX together forms side TW thus,

• TX + WX = 45
• 15 + WX = 45
• WX = 45-15
• WX = 30

and,

• TX/WX = 15/30
• TX/WX = 1/2

since TX and WX are in a ratio of 1:2 thus, UV and VW would be in the same ratio as well.

Now ,In order to find the measure of UV, we can assume UV as x and VW as 2x ,then,

• x + 2x = 63
• 3x = 63
• x = 63/3
• x = 21

Therefore, the measure of UV is 21 units.

Answer 2

UV = 21

Explanation:

Since
`\overline{\sf TU}` is parallel to
`\overline{\sf VX}`, we can use the Triangle Proportionality Theorem to find the length of UV.

The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally.

In the given triangle, line segment VX is parallel to side TU, so VX divides sides UW and TW proportionally.

Therefore, according to the Triangle Proportionality Theorem:

`\sf \overline{UV}:\overline{UW}=\sf \overline{TX}:\overline{TW}`

Given that:

• 
  `\sf \overline{UW}=63`
• 
  `\sf \overline{TX}=15`
• 
  `\sf \overline{TW}=45`

Substitute these values into the proportion and solve for UV:

`\begin{aligned}\sf \overline{UV}:\overline{UW}&=\sf \overline{TX}:\overline{TW}\\\\\overline{\sf UV}:63&=15:45\\\\\frac{\overline{\sf UV}}{63}&=(15)/(45)\\\\\overline{\sf UV}&=(15)/(45) \cdot 63\\\\\overline{\sf UV}&=(945)/(45)\\\\\overline{\sf UV}&=21\end{aligned}`

So, the length of UV is 21.