We get the length of QS as 102 units.
We are given two equations:
QR = 4 x +7, and RS = 8 x - 37
We are also told that R is the mid point of QS.
This means that R will divide QS in two equal halves.
This also implies that:
QR = RS
Substituting the values, we get that:
4 x + 7 = 8 x - 37
Solving for x, we get that:
8 x - 4 x = 7 + 37
4 x = 44
x = 44 / 4
x = 11
Now substituting the value of x in QR and RS to find the length of QS:
QR = 4 x + 7 = 4 ( 11 ) + 7 = 44 + 7 = 51
RS = 8 x - 37 = 8 ( 11 ) - 37 = 88 - 37 = 51
QS = QR + RS
QS = 51 + 51 = 102
Therefore, we get the length of QS as 102 units.
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