The points Q, R, S and T all lie on the same line segment, in that order, such that the ratio of Q, R, colon, R, S, colon, S, TQR:RS:ST is equal to 1, colon, 1, colon, 3, .1:1:3. If Q, T, equals, 10, commaQT=10, find R, T, .RT.

Answer 1

Since the ratio QR:RS:ST is 1:1:3, we can express the lengths of the segments as follows:

QR = x
RS = x
ST = 3x

Given that QT = 10, we have:

QT = QR + RS + ST
10 = x + x + 3x
10 = 5x
x = 2

Therefore, QR = RS = 2 and ST = 6.

Now, RT = RS + ST = 2 + 6 = 8.

Therefore, RT = 8.