Question: The triangle ABC is an isosceles triangle whose perimeter is 39. Triangle ABD is an equilateral triangle whose perimeter is 33. What is the length of the base of the isosceles triangle?

Solution:

Let AB be x

Because ABC is an isosceles triangle (given),

so, AB = AC = x

Because ABD is an equilateral triangle (given),

so, AB = BD = DA = x

Because the perimeter of the equilateral triangle is 33 (given),

so, 3x = 33, so x = 11

Because the perimeter of the isosceles triangle is 39 (given),

so, 2x + BC = 39

BC = 39 - 2x = 39 - 2(11) = 39 - 22 = 17

Therefore, the length of the base of the triangle ABC is 17.