The base of the isosceles triangle is 80 mm, and the perimeter of the triangle is 196 m. Calculate the height drawn to the base.

1. Determine the total length of the two lateral sides of an isosceles triangle:

196 – 80 = 116 mm;

2. Determine the length of the lateral side of an isosceles triangle:

116: 2 = 58 mm;

3. Since the height drawn to the base of the isosceles triangle divides it in half, we define half of the base of the triangle, which will simultaneously be the leg of the formed right triangle:

80: 2 = 40 mm;

4. Since the height is the second leg of the formed right-angled triangle, we determine it using the Pythagorean theorem:

√ (58) ² – (40) ² = √3364 – 1600 = √1764 = 42 mm.

Answer: the height drawn to the base is 42 millimeters.