Triangle $ABC$ is an isosceles triangle with vertex angle $B. \,AB$= \[5x - 28\], AC= \[x + 5\] and $BC$= \[2x + 11\]. How do you find the length of the base?

Hint: Given is an isosceles triangle. This triangle has base angles the same so that the opposite sides are of the same length. So we will equate AB and BC. Then we will find the value of $x$ and then we will put that value of $x$ in the base equation and find the base length.

Complete step by step answer:
Given that, Triangle ABC is an isosceles triangle with vertex angle B. Vertex angle at B means the two sides with B as one of the vertex will be the same, that is AB and BC are the two sides of this isosceles triangle are the same. So we will equate the sides,

Now ,
\[5x - 28 = 2x + 11\]
Taking variable son one side,
\[5x - 2x = 11 + 28\]
\[3x = 39\]
On dividing both sides by 3 we get,
\[x = 13\].
Now putting this value of x in the equation of base we get,
\[x + 5 = 13 + 5 = 18\].

Thus the length of base AC is 18 units.

Note: This problem is totally based on the concept that the triangle is isosceles. No other clue is there. vertex at $b$ is the other data that is to be noted. If we were given the perimeter of the triangle then we might have used the equation as sum of all sides equating to the perimeter and then finding the value of $x$. The Scalene triangle has all sides of different length and the equilateral triangle has all sides of the same length.