Question

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

Answer 1

Answer:

42 units

Step-by-step explanation:

If R is the midpoint of QS, then by definition, QR = RS. Since QR = 8x - 51 and RS = 3x - 6, set these equal to solve for x:

QR = RS

8x - 51 = 3x - 6

5x = 45

x = 9

Now that we know x = 9, we can plug this back into one of the expressions for QR or RS to find its length:

QR = 8x - 51 = 8 * 9 - 51 = 72 - 51 = 21

Since half of QS is 21, then the whole of QS is twice that:

2 * 21 = 42

The answer is thus 42 units.

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