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In RST, RU≅US and RV≅VT, If UV, the midsegment, is equal to 2x - 2 and

ST = 8x - 28, find the value of x. Show all work for credit.

In RST, RU≅US and RV≅VT, If UV, the midsegment, is equal to 2x - 2 and ST = 8x - 28, find-example-1
User Uros
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2 Answers

6 votes

Check the picture below.


\stackrel{m}{2x-2}~~ = ~~\cfrac{\stackrel{base}{8x-28}}{2}\implies 4x-4=8x-28\implies -4=4x-28 \\\\\\ 24=4x\implies \cfrac{24}{4}=x\implies 6=x

In RST, RU≅US and RV≅VT, If UV, the midsegment, is equal to 2x - 2 and ST = 8x - 28, find-example-1
User Clete
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8.2k points
3 votes

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:


\sf UV = (ST)/(2)

Substitute the value of UV and ST, we get


\sf 2x - 2 = (8x - 28)/(2)

Multiplying both sides by 2, we get:


\sf 2(2x - 2)= (8x - 28)/(2)* 2

Simplify:


\sf 4x - 4 = 8x - 28

Subtracting 4x from both sides, we get:


\sf 4x - 4 -4x= 8x - 28 - 4x


\sf -4 = 4x - 28

Adding 28 to both sides, we get:


\sf -4 +28= 4x - 28+28


\sf 24 = 4x

Dividing both sides by 4, we get:


\sf ( 24 )/(4) = (4x)/(4)


\sf x = 6

Therefore, the value of x is 6.

User Revelt
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