Question

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 problem have? What if we said that point b lies on the line defined by points a and c?

Answer 1

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

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

... AC = 10.3 cm

b) If B is not on the segment AC, there can only be one solution: C must lie on AB. Then ...

... AC = 7.8 cm - 2.5 cm

... AC = 5.3 cm

This, together with the solution of Part (a) means there are two solutions.

Answer 2

Answer:

(i) one solution,

ac = 10.3 cm

(ii) two solution,

ac = 10.3 cm or 5.3 cm

Step-by-step explanation:

(i) If b lies on the line segment ac,

Then,

ac = ab + bc,

Thus, there is only one solution of this problem,

(ii) While if b lies on the line defined by points a and c,

Then there can be three cases,

Case 1 : b is between a and c,

⇒ ac = ab + bc

Case 2 : c is between a and b

⇒ ac = ab - bc

( not possible because ab < bc )

Case 3 : a is between b and c,

⇒ ac = bc - ab

Here, ab=7.8 cm, bc=25mm = 2.5 cm,

∵ 1 cm = 10 mm

Thus, the possible solutions are,

ac = 10.3 cm or 5.3 cm