Find st if s is between r and t, sr = 2x + 7, st = x - 6, and rt = 100

A line segment can be divided into subsegments by having points on the line segment. The value of ST is 27 units.

Given that:

If S is between R and T, then:

So, we have:

Collect like terms

Divide through by 3

Recall that:

Hence, the value of ST is 27 units.

Read more about lines and points at:

link

just needed some points but try socratic

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4