Question

The points T, U, V, and W all lie on the same line segment, in that order, such that the ratio of TU : UV : VW is equal to 4:4:3. If TW = 22, find UV.

A. 8

B. 10

C. 12

D. 14

Answer 1

The length UV is 8 units.

Step-by-step explanation:

We are given that the ratio of TU : UV : VW is equal to 4:4:3. Let's assign a value to TU using the ratio. Since the total ratio is 4+4+3=11, we can say that TU represents 4/11 of the total length. So, TU = (4/11) * TW = (4/11) * 22 = 8.

Since TU + UV + VW = TW, we can substitute the known values: 8 + UV + 3/11 * TW = TW. Solving for UV, we get UV = TW - TU - VW = 22 - 8 - 3/11 * 22 = 22 - 8 - 6 = 8.

Therefore, UV = 8, which corresponds to option A.