7) (x, TU, TB) = (4, 8, 13)
9) (x, RS, MN) = (8, 41, 41)
11) (AB, BC, AC) = (42, 42, 84)
What are the values of the variable x and the lengths of the line segments?
In this question we have three cases of colinear line segments, each of them can be solved by using definitions from Euclidean geometry and algebraic handling:
Case 7 - TU = 2 · x, UB = 3 · x + 1, TB = 21
TB = TU + UB
21 = 2 · x + 3 · x + 1
21 = 5 · x + 1
5 · x = 20
x = 4
Then, the lengths of each line segment are:
TB = 21
TU = 2 · 4
TU = 8
UB = 3 · 4 + 1
UB = 13
The solutions are (x, TU, TB) = (4, 8, 13).
Case 9 - RS = 3 · x + 17, MN = 7 · x - 15
RS = MN
3 · x + 17 = 7 · x - 15
4 · x = 32
x = 8
And the lengths of each line segment are:
RS = MN = 41
The solutions are (x, RS, MN) = (8, 41, 41).
Case 11 - AB = 2 · x - 8, BC = x + 17
AB + BC = AC
AB = BC
2 · x - 8 = x + 17
x = 25
And the lengths of each line segment are:
AB = 2 · 25 - 8
AB = 42
BC = AB
BC = 42
AC = 42 + 42
AC = 84
The solutions are (AB, BC, AC) = (42, 42, 84).
To learn more on line segments: https://brainly.com/question/25727583
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