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 1:5:2. If TW=32, find UW.

Answer 1

Answer:

Answer:

UV = 10UV=10

Step-by-step explanation:

Given

TU : UV : VW = 2 : 5 : 5TU:UV:VW=2:5:5

TW = 24TW=24

Required

Determine UV

From the given parameters, we have that:

Ratio of TU = 2

Ratio of UV = 5

Ratio of VW = 5

First, we have to add up the total ratio;

Total = Ratio of TU + Ratio of UV + Ratio of VW

Total = 2 + 5 + 5Total=2+5+5

Total = 12Total=12

Next is to calculate the length of UV; as follows;

UV = \frac{Ratio\ of\ UV}{Total\ Ratio} * TWUV=Total RatioRatio of UV∗TW

Substitute 5 for Ratio of UV;  12 for Total Ratio and 24 for TW

UV = \frac{5}{12} * 24UV=125∗24

UV = \frac{5 * 24}{12}UV=125∗24

UV = \frac{120}{12}UV=12120

UV = 10UV=10

Hence; length of UV is 10 units