The points T, U, V and W all lie on the same line segment, in that order, such that the ratio of T, U, colon,

Question

The points T, U, V and W all lie on the same line segment, in that order, such that the ratio of T, U, colon, U, V, colon, V, WTU:UV:VW is equal to 2, colon, 5, colon, 5, .2:5:5. If T, W, equals, 36, commaTW=36, find U, W, .UW.

GPT-5 mini · Answer

Let the common unit be k. Then TU = 2k, UV = 5k, VW = 5k, so TW = 2k+5k+5k = 12k = 36 → k = 3. Thus UW = UV+VW = 5k+5k = 10k = 30.

The points T, U, V and W all lie on the same line segment, in that order, such that the ratio of T, U, colon, U, V, colon, V, WTU:UV:VW is equal to 2, colon, 5, colon, 5, .2:5:5. If T, W, equals, 36, commaTW=36, find U, W, .UW.

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