Question

Please anwser these two questions please

Answer 1

x = 25, AB = 42, BC = 42, AC = 84

x = 4, AB = 49, BC = 49, AC = 98

Explanation:

The midpoint of a line segment is the point that is equidistant from both endpoints of the line segment.

It divides the line equally in two parts.

So, In first case:

AB = BC

Substitute the value:

2x -8 = x + 17

Add 8 on both sides

2x - 8 + 8 = x + 17 + 8

2x = x + 25

Subtract x on both sides:

2x - x = x + 25 - x

x = 25

Therefore,

x = 25

AB = 2 × 25 - 8 = 50 - 8 = 42

BC = 25 + 17 = 42

AC = AB + BC = 42 + 42 = 84

Similarly

In second case:

AB = BC

AC = AB + BC

Substitute the value:

3x - 31 = x + 6 + x + 6

Simplify like terms:

3x - 31 = 2x + 12

Add 31 on both sides

3x - 31 + 31 = 2x + 12 + 31

3x = 2x + 43

Subtract 2x on both sides:

3x - 2x = 2x + 43 - 2x

x = 43

Therefore,

x = 43

AB = 43 + 6 = 49

BC = 43 + 6 = 49

AC = 49 + 49 = 98

Answer 2

see explanation

Explanation:

given B is the midpoint of AC , then

AB = BC ( substitute values )

2x - 8 = x + 17 ( subtract x from both sides )

x - 8 = 17 ( add 8 to both sides )

x = 25

Then

AB = 2x - 8 = 2(25) - 8 = 50 - 8 = 42

BC = x + 17 = 25 + 17 = 42

AC = AB + BC = 42 + 42 = 84

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Similarly

AB = BC = x + 6 and

AC = AB + BC ( substitute values )

3x - 31 = x + 6 + x + 6 ( simplify right side )

3x - 31 = 2x + 12 ( subtract 2x from both sides )

x - 31 = 12 ( add 31 to both sides )

x = 43

Then

AB = x + 6 = 43 + 6 = 49

BC = AB = 49

AC = AB + BC = 49 + 49 = 98