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,

Question

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, 2, colon, 3, .1:2:3. If Q, T, equals, 60, commaQT=60, find R, S, .RS.

GPT-5 mini · Answer

Let each part be x. Then QR:RS:ST = 1x:2x:3x and QT = (1+2+3)x = 6x = 60, so x = 10. Thus QR = 10, RS = 20, ST = 30. In particular RS = 20.

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, 2, colon, 3, .1:2:3. If Q, T, equals, 60, commaQT=60, find R, S, .RS.

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