ABC is an isoscelea triangle with AB =AC and its perimeter is 64cm .the altitude from A to BC is 24cm.find the length of AC and BC?

Answer 1

Let AB=AC = x, and the base BC = 2y
Then you have
2x+2y = 64
y^2 + 24^2 = x^2

(32-x)^2 + 24^2 = x^2
x = 25

You might have guessed this right off, since one of the basic right triangles with integer sides is

7-24-25

Of course, a 3-4-5 triangle scaled up by 6 would be 18-24-40 but that gives too large a perimeter.