Question

If R is the midpoint of QS, QR= 8x-51 and RS=3x-6, find QS.

Answer 1

QS = 11x - 57

since r is the midpoint, QR + RS = QS

Answer 2

Answer: The required length of QS is 42 units.

Step-by-step explanation: Given that R is the midpoint of QS, where

`QS=8x-51,~~RS=3x-6.`

We are to find the length of QS.

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

`QR=RS\\\\\Rightarrow 8x-51=3x-6\\\\\Rightarrow 8x-3x=51-6\\\\\Rightarrow 5x=45\\\\\Rightarrow x=(45)/(5)\\\\\Rightarrow x=9.`

Therefore, the length of QS is given by

`QS\\\\=QR+RS\\\\=8x-51+3x-6\\\\=11x-57\\\\=11*9-57\\\\=99-57\\\\=42.`

Thus, the required length of QS is 42 units.