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LejlaDolic

Since R is the midmoint of QS that means that QR and RS are equal to each other. So first you need to find x. There are many different ways to set up the equation to solve for x, but I'll show you the easiest one:

QR+QS=RT+QR

(2x-4)+(2x-4)=(8x-43)+(2x-4)

Combine like terms:

4x-8=10x-47

Isolate Variable:

4x-8=10x-47

-4x -4x

6x-47=-8

Isolate Constant:

6x-47=-8

+47 +47

6x=39

Divide:

x=6.5

Check Your Answer:

(Plug in 6.5 as x)

(4(6.5)-8)=(8(6.5)-43)+(2(6.5)-4)

18=18

Answer:

The measure of QS is 68 units.

Step-by-step explanation:

Given information: R is midpoint of QS, RS=2x-4, ST=4x-1, and RT=8x-43.

We need to find the value of QS.

From the given figure it is clear that points Q, R, S and T are collinear.

[tex]RT=RS+ST[/tex]

[tex]8x-43=(2x-4)+(4x-1)[/tex]

On combining like terms.

[tex]8x-43=(2x+4x)+(-4-1)[/tex]

[tex]8x-43=6x-5[/tex]

Isolate variable terms.

[tex]8x-6x=43-5[/tex]

[tex]2x=38[/tex]

Divide both sides by 2.

[tex]x=19[/tex]

The value of x is 19.

It is given that R is midpoint of QS. It means R divides the line QS in two equal parts.

[tex]QS=2(RS)[/tex]

[tex]QS=2(2x-4)[/tex]

Substitute x=19 in the above equation.

[tex]QS=2(2(19)-4)[/tex]

[tex]QS=2(38-4)[/tex]

[tex]QS=2(34)[/tex]

[tex]QS=68[/tex]

Therefore the measure of QS is 68 units.

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