Given the equilateral triangle ABC and the isosceles triangle DBC, what is AB+DB if the perimeter of DBC is 50 and BC=24?

Consider the isosceles triangle DBC with BC = 24 and a
perimeter of 50.  Assuming 24 is the unique side of the triangle, you can write the
following equation:

CD + DB + BC =
50

CD + DB + 24 = 50

CD + DB +
24 = 50

CD + DB = 26

These
sides are equal because it is an isosceles triangle, so they each equal
13.

Therefore, DB = 13

Since
triangle ABC is equilateral and BC = 24, then AB = 24.

AB +
DB

24 + 13 =
37

Solution: 
37

**Note**

This
was assuming BC is the unique side of the isosceles triangle.  If BC is one of the
matching sides of the isosceles triangle, the answer
changes.

CD + DB + BC = 50

24
+ DB + 24 = 50

DB + 48 = 50

DB
= 2

AB + DB

24 + 2 =
26

Another possible answer is 26.