The perimeter of an isosceles triangle is 50 and its lateral side is 17. Find the area of the triangle.

AC = CB = 17
Perimeter of Triangle = 50
AB = 50 – AC – CB = 50 – 17 – 17 = 16.
The height of the triangle, lowered from the top to the base, is also the median, i.e. AH = HB = AB / 16 = 8
The START triangle is rectangular, according to the Pythagorean theorem we express CH:
CH = (17 ^ 2 – 8 ^ 2) ^ 0.5
CH = 15
Triangle area = 1/2 * CH * AB = 1/2 * 15 * 16 = 120