Answer:
Value of BC is 25 units.
Step-by-step explanation:
Given: AC = 2x+23 units , AB = 4x+1 units and BC = 3x-8 units.
Isosceles triangle states that a triangle with two congruent sides and congruent base angles.[Congruent means equal]
Since, in the given triangle ABC [tex]\angle B = \angle C[/tex] i.e, base angles are equal.
By definition of isosceles triangle,
⇒ΔABC is an isosceles triangle
[tex]AB = AC[/tex]
4x + 1 = 2x + 23
Subtract 2x from both sides we get;
4x + 1 -2x = 2x + 23 -2x
Simplify:
2x + 1= 23
Subtract 1 from both sides we get;
2x +1 -1 = 23-1
Simplify:
2x = 22
Divide both sides by 2 we get;
x = 11
BC = 3x -8 = 3(11) - 8 = 33 -8 = 25 units
Therefore, the value of side BC is, 25 units.
