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

$QR=RS\\\\\Rightarrow 8x-51=3x-6\\\\\Rightarrow 8x-3x=51-6\\\\\Rightarrow 5x=45\\\\\Rightarrow x=\dfrac{45}{5}\\\\\Rightarrow x=9.$

Therefore, the length of QS is given by

$QS\\\\=QR+RS\\\\=8x-51+3x-6\\\\=11x-57\\\\=11\times9-57\\\\=99-57\\\\=42.$

Thus, the required length of QS is 42 units.