In a triangle, the bisector divides the base in half. How many times is the sum of the squares of the sides

In a triangle, the bisector divides the base in half. How many times is the sum of the squares of the sides of the triangle from the product of the same sides?

Since the bisector BН divides the opposite side in half, then this bisector is also the median of the triangle, which is possible if the triangle ABC is isosceles.

Then AB = BC.

Let AB = BC = X cm.

Then AB ^ 2 + BC ^ 2 = X ^ 2 + X ^ 2 = 2 * X ^ 2.

AB * BC = X * X = X2.

Let us determine the ratio of the sum of squares and the product of the sides.

(AB ^ 2 + BC ^ 2) / AB * BC = 2 * X ^ 2 / X ^ 2 = 2.

Answer: The ratio of the sum of squares and the product of the sides is 2.