Point b lies on the segment ac . Find the length of the segment ac, if ab=7.8 cm, bc=25mm. How many different solutions can this

a) If B falls between A and C, there is only one solution:

... AC = AB + BC = 7.8 cm + 2.5 cm

... AC = 10.3 cm

b) If B is outside of the segment AC, there will still only be one solution: C must be positioned on AB. Thus...

... AC = 7.8 cm - 2.5 cm

... AC = 5.3 cm

This, along with the result of Part (a), provides two solutions.

Answer:

(i) one solution,

ac = 10.3 cm

(ii) two solutions,

ac = 10.3 cm or 5.3 cm

Step-by-step explanation:

(i) If b is located within the line segment ac,

Then,

ac = ab + bc,

Hence, there is solely one solution for this scenario,

(ii) However, if b is on the line traced by points a and c,

There could be three scenarios,

Case 1: b is positioned between a and c,

⇒ ac = ab + bc

Case 2: c is situated between a and b

⇒ ac = ab - bc

( not feasible since ab < bc )

Case 3: a is found between b and c,

⇒ ac = bc - ab

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ac = 10.3 cm or 5.3 cm