Question

The points S, T, U and V all lie on the same line segment, in that order, such that the

Answer 1

Answer: TV = 10

==============================================

Explanation

Let x be some positive real number such that

• ST = 6x
• TU = 2x
• UV = 3x

leading to the ratio

ST:TU:UV = 6x:2x:3x = 6:2:3

Note how I effectively started with 6:2:3 and multiplied all parts of the ratio by x to get 6x:2x:3x

-----------------

The parts of the ratio add up to the longest segment SV

ST+TU+UV = SV

6x+2x+3x = 22

11x = 22

x = 22/11

x = 2

Therefore,

• ST = 6x = 6*2 = 12
• TU = 2x = 2*2 = 4
• UV = 3x = 3*2 = 6

Note how ST+TU+UV = 12+4+6 = 22, which is the length of SV. This helps confirm we have the correct x value.

-----------------

The last step is to find the length of TV

TV = TU+UV

TV = 4+6

TV = 10

Or you could do

ST + TV = SV

12+TV = 22

TV = 22-12

TV = 10