Respuesta :

moab5996

QS would be 42. So the way i did it was I:

8x-51=3x-6

x=9

Plugged into both equations of QR and RS to then get the answer of 42

Answer:  The required length of QS is 42 units.

Step-by-step explanation:  Given that the point R is the midpoint of the line segment QS,

where QR= 8x-51 and RS = 3x-6.

We are to find the length of QS.

Since R is the midpoint of the segment QS, so we must have

[tex]QR=RS\\\\\Rightarrow 8x-51=3x-6\\\\\Rightarrow 8x-3x=51-6\\\\\Rightarrow 5x=45\\\\\Rightarrow x=\dfrac{45}{5}\\\\\Rightarrow x=9.[/tex]

Therefore, the length of QS is given by

[tex]QS\\\\=QR+RS\\\\=8x-51+3x-6\\\\=11x-57\\\\=11\times9-57\\\\=99-57\\\\=42.[/tex]

Thus, the required length of QS is 42 units.

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