Find the length of the base of an isosceles triangle whose side is √17 and whose area is 4.

We use the formula for finding the area of an isosceles triangle through its sides:
S = (b / 4) * √ (4 * a ^ 2 – b ^ 2), where b is the base of the triangle, a is the side of the triangle;
Substitute the known values into the formula and find the base length:
4 = (b / 4) * √ (4 * (√17) ^ 2-b ^ 2);
16 = b * √ (4 * 17 – b ^ 2);
16 = b * √ (68 – b ^ 2);
(16 / b) ^ 2 = 68 – b ^ 2;
b ^ 4-68 * b ^ 2 + 256 = 0, let’s take b ^ 2 = y;
y ^ 2-68 * y + 256 = 0, we solve the quadratic equation;
D = 68 * 68-4 * 256 = 3600;
y1 = (68 + 60) / 2 = 64; b1 = 8;
y2 = (68-60) / 2 = 4; b2 = 2;
Answer: the base length is 8 or 2.