Question: ABC is an isosceles triangle. BC = 9, CD is a median. CD divide the perimeter of the triangle ABC into two parts. The difference of the two parts is 5. What is the side of the triangle?

Solution:

Because ABC is an isosceles triangle (given),

so, AB = AC = x

Because CD is a median (given),

so, AD = BD = x/2

Because CD cut the perimeter into two parts and the difference of these two parts is 5 (given),

so, we get the equation:

9 + x/2 - (x/2 + x) = 5

9 + x/2 - x/2 - x = 5

x = 9 - 5 = 4

if x = 4, can not make a triangle, because 4 + 4 < 9.

The sum of length of the two sides of a triangle must be large than the length of the third side.

So, we get the equation:

x + x/2 - (x/2 + 9) = 5

x + x/2 - x/2 - 9 = 5

x = 5 + 9 = 14

So, the length of the side of the isosceles triangle is 14.