Question

Find length of the side AB in the below figure.

a.2
b.3
c.4
d.5

Answer 1

Hint: The definition of the angle bisector of a triangle is a line segment that bisects one of the vertex angles of a triangle. In general, an angle bisector is equidistant from the sides of the angle when measured along a segment perpendicular to the sides of the angle.
Complete step by step answer:
In the figure, given that XY is the perpendicular bisector of side AB of the triangle ABC. From the figure, the length of the side AC is 7 units and the length of AO is 2 units. The given triangle ABC has two equal sides.
The definition of the angle bisector of a triangle, so the perpendicular bisector cuts the side AB into two equal parts.
Therefore AB = AO + OB
AO = OB = 2.
AB = 2 + 2 = 4
Hence the length of the side AB is 4 units.
Therefore, the correct option of the given question is option (c).
Note: The perpendicular bisector of a side of a triangle is a line perpendicular to the side and passing through its midpoint. The three perpendicular bisectors of the sides of a triangle meet in a single point, called the circumcenter. The circumcenter is equidistant from the vertices of the triangle.