The perimeter of an isosceles triangle is 250 and the side is 85. Find the area of the triangle.

Equal.treg = a + 2b
Substitute the known values ​​and get:
250 = a + 2 * 85
250 = a + 170
250 – 170 = a
80 = a

AC = a = 80

Let’s draw the height BH. By theorem: the height of an isosceles triangle is both the bisector and the median. The height is perpendicular to the base, which means it will divide it in half.
AC = AH + HC
AH = HC = 1/2 AC
AH = 80: 2
AH = 40

Consider a triangle ABH. the angle BHA is straight, so the triangle is right-angled. Let’s use the Pythagorean theorem:
AB ^ 2 = BH ^ 2 + AH ^ 2
BH ^ 2 = AB ^ 2 – AH ^ 2
BH ^ 2 = 85 ^ 2 – 40 ^ 2
BH ^ 2 = (85 – 40) ^ 2
BH ^ 2 = (85 – 40) * (85 + 40)
BH ^ 2 = 45 * 125
BH ^ 2 = 5625
BH = root of 5625
BH = 75

Comparable triples = 1/2 * a * h
Comparable triples = 1/2 * 80 * 75
Comparable triples = 6000/2
Comparable triples = 3000

Answer: 3000