Answer:
x = 6
Explanation:
Given:
In RST, RU≅US and RV≅VT
UV the mid-segment, is equal to 2x - 2 and ST = 8x - 28
To find:
value of x
Solution:
Since In triangle RST, UV is the mid-segment, so it is parallel to ST. This means that the triangle UVT is similar to the triangle RST.
Note:
A mid-segment of a triangle is a line segment that connects the midpoints of two sides of the triangle. A mid-segment is parallel to the third side of the triangle and is half as long as the third side.
This means that:

Substitute the value of UV and ST, we get

Multiplying both sides by 2, we get:

Simplify:

Subtracting 4x from both sides, we get:


Adding 28 to both sides, we get:


Dividing both sides by 4, we get:


Therefore, the value of x is 6.